// Numbas version: exam_results_page_options
{"name": "Ratio & Proportion", "feedback": {"allowrevealanswer": true, "showtotalmark": true, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "showanswerstate": true, "showactualmark": true}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "<p>Ratio and Proportion</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Q1 Intro to Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num11", "ans11", "ans12", "k", "num12", "boy", "number0", "number1", "number2", "low", "ans21", "ans22", "ans23", "l", "girl", "student", "ans31", "ans32", "ans33"], "tags": ["rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Watch the following video to understand ratios better!</p>\n<p><a href=\"http://www.mathtutor.ac.uk/arithmetic/ratios/video\">Ratios Video</a></p>\n<p></p>\n<p>Part 1:</p>\n<p>Divide both numbers by their highest common&nbsp;factor</p>\n<p></p>\n<p>Part 2:</p>\n<p>Divide both the number of boys and girls&nbsp;by their highest common&nbsp;factor</p>\n<p>$\\frac{\\var{boy}}{\\var{l}}$ : $\\frac{\\var{girl}}{\\var{l}}$</p>\n<p>$\\var{ans21}$ : $\\var{ans22}$</p>\n<p></p>\n<p>$\\frac{\\var{student}}{\\var{boy} + \\var{girl}} \\times \\var{girl} = \\var{ans23}$</p>\n<p></p>\n<p>Part 3:</p>\n<p>First get the lowest common denominator = $\\var{low}$</p>\n<p>$(\\frac{\\var{low}}{\\var{number0}}) \\times&nbsp;1 = \\var{ans31}$</p>\n<p>$(\\frac{\\var{low}}{\\var{number1}}) \\times&nbsp;5 = \\var{ans32}$</p>\n<p>$(\\frac{\\var{low}}{\\var{number2}}) \\times&nbsp;7 = \\var{ans33}$</p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Express the ratio $\\var{num11}$ : $\\var{num12}$ in its simplest form.</p>\n<p>[[0]]:[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>To express a ratio in its simplest form you always multiply or divide all parts by the same number.</p>\n<p>In this case you need to divide the ratios by a common factor. Can both numbers be divided by 2? Or maybe 3 or 4? Keep dividing both sides until you think it can't get any simpler.</p>\n<p>Alternatively you could find the highest common factor and divide by that.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>In a class there are $\\var{boy}$ boys and&nbsp;$\\var{girl}$ girls. Find the ratio of boys to girls in the class in its simplest form.</p>\n<p>[[0]]boys :&nbsp;[[1]]girls</p>\n<p>If the whole year group of&nbsp;$\\var{student}$ students is in the same ratio, how many girls are there in the year?</p>\n<p>[[2]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Express this ratio in its simplest form as above. Divide the&nbsp;$\\var{student}$ students into this ratio.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}", "minValue": "{ans23}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Express $\\frac{1}{\\var{number0}}:\\frac{5}{\\var{number1}}:\\frac{7}{\\var{number2}}$ as a ratio in whole numbers.</p>\n<p></p>\n<p>[[0]]&nbsp;: [[1]]&nbsp;: [[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>This time we want to get rid of the fractions. To do this we will multiply all the parts by a number. Find the Lowest Common Multiple of the denominators (if its difficult to find you can always multiply the three denominators and use that). Multiply all the fractions by this number. Simplify your answer ratio into its simplest form as above.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}", "minValue": "{ans33}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following ratio questions:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"boy": {"definition": "ans21*l", "templateType": "anything", "group": "Ungrouped variables", "name": "boy", "description": ""}, "number0": {"definition": "random(2,3,4,6)", "templateType": "anything", "group": "Ungrouped variables", "name": "number0", "description": ""}, "k": {"definition": "random(6..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "num11": {"definition": "ans11*k", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "l": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "ans31": {"definition": "(low/number0)*1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans22": {"definition": "random(3,4,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans12": {"definition": "random([5,7,11,13])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "random([1,2,3,4])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "num12": {"definition": "ans12*k", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "low": {"definition": "lcm([number0,number1,number2])", "templateType": "anything", "group": "Ungrouped variables", "name": "low", "description": ""}, "student": {"definition": "random(4..7)*(boy+girl)", "templateType": "anything", "group": "Ungrouped variables", "name": "student", "description": ""}, "number1": {"definition": "random(8,9,11,12)", "templateType": "anything", "group": "Ungrouped variables", "name": "number1", "description": ""}, "number2": {"definition": "random(10,13,15,16)", "templateType": "anything", "group": "Ungrouped variables", "name": "number2", "description": ""}, "ans32": {"definition": "(low/number1)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "(low/number2)*7", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans23": {"definition": "(student/(boy+girl))*girl", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "girl": {"definition": "ans22*l", "templateType": "anything", "group": "Ungrouped variables", "name": "girl", "description": ""}, "ans21": {"definition": "random([3,4,5] except {ans22})", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}}, "metadata": {"description": "<p>Simplifying ratios</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q2 Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["material", "numberone", "numbertwo", "numberthree", "ansone", "ratio", "anstwo", "ansthree", "lent", "summ", "numberfour", "total", "ansfour", "ansfive", "anssix", "money", "ratioab", "ratioc", "ans31", "ans32", "ans33", "numberone1", "numbertwo1", "k"], "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p>Part 1:</p>\n<p>Add the ratio numbers and then divide the length by the summed total</p>\n<p><span class=\"re2\">$\\frac{\\var{lent}}{\\var{summ}}$</span></p>\n<p><span class=\"sy0\">Then multiply each peice by the ratio length</span></p>\n<p><span class=\"sy0\">$\\var{numberone} \\times \\var{ratio}$</span></p>\n<p><span class=\"sy0\">$\\var{numbertwo} \\times&nbsp;\\var{ratio}$</span></p>\n<p><span class=\"sy0\">$\\var{numberthree} \\times&nbsp;\\var{ratio}$</span></p>\n<p><span class=\"sy0\"></span></p>\n<p><span class=\"sy0\">Part 2:</span></p>\n<p><span class=\"sy0\">Use the same method as in part 1</span></p>\n<p><span class=\"sy0\">$\\frac{\\var{total}}{(\\var{numberone1}+\\var{numbertwo1}+\\var{numberfour})}$</span></p>\n<p><span class=\"sy0\">$\\var{numberone} \\times \\var{k}$</span></p>\n<p><span class=\"sy0\">$\\var{numbertwo} \\times \\var{k}$</span></p>\n<p><span class=\"sy0\">$\\var{numberfour} \\times \\var{k}$</span></p>\n<p><span class=\"sy0\"></span></p>\n<p>Part 4:</p>\n<p>$(\\frac{\\var{money}}{(\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc})}) \\times&nbsp;\\var{ratioab[0]} = \\var{ans31}$</p>\n<p>$(\\frac{\\var{money}}{(\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc})}) \\times&nbsp;\\var{ratioab[1]} = \\var{ans32}$</p>\n<p>$(\\frac{\\var{money}}{(\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc})}) &nbsp;\\times&nbsp;\\var{ratioc}&nbsp;= \\var{ans33}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>A piece of $\\var{material}$ $\\var{lent}$ cm long is cut into three pieces&nbsp;in the ratio of $\\var{numberone}$ to $\\var{numbertwo}$ to $\\var{numberthree}$. Determine the lengths of the three pieces.</p>\n<p>[[0]]cm</p>\n<p>[[1]]cm</p>\n<p>[[2]]cm</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Imagine that the $\\var{material}$ is divided into&nbsp;$\\var{numberone}$ +&nbsp;$\\var{numbertwo}$ +$\\var{numberthree}$ pieces. The first piece should be&nbsp;$\\var{numberone}$ times its length. The second piece should be&nbsp;$\\var{numbertwo}$ times this length. The third piece should be&nbsp;$\\var{numberthree}$ times this length.</p>\n<p>Double check: When you add up your pieces they should add to&nbsp;$\\var{lent}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ansone}", "strictPrecision": false, "minValue": "{ansone}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{anstwo}", "strictPrecision": false, "minValue": "{anstwo}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ansthree}", "strictPrecision": false, "minValue": "{ansthree}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Divide $\\var{total}$ in the ratio $\\var{numberone1}$:$\\var{numbertwo1}$:$\\var{numberfour}$.</p>\n<p>[[0]]</p>\n<p>[[1]]</p>\n<p>[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Divide&nbsp;$\\var{total}$ &nbsp;into&nbsp;$\\var{numberone1}$ &nbsp;+&nbsp;$\\var{numbertwo1}$ &nbsp;+&nbsp;$\\var{numberfour}$ parts. Each of these parts contain $\\var{k}$.</p>\n<p>Find&nbsp;$k&nbsp;\\times \\var{numberone}$</p>\n<p>Find&nbsp;$k&nbsp;\\times \\var{numbertwo}$</p>\n<p>Find&nbsp;$k&nbsp;\\times \\var{numberfour}$</p>\n<p>To double check, add these results together. You should get&nbsp;$\\var{total}$.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ansfour}", "minValue": "{ansfour}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ansfive}", "minValue": "{ansfive}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{anssix}", "minValue": "{anssix}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Divide &euro;$\\var{money}$ in the ratio $\\var{ratioab[0]}:\\var{ratioab[1]}:\\var{ratioc}$</p>\n<p><em>(Calculate to 2&nbsp;decimal place!!)</em></p>\n<p>&euro;[[0]] : &euro;[[1]] : &euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Just as before, add all parts together and divide by this.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "strictPrecision": false, "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "strictPrecision": false, "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}", "strictPrecision": false, "minValue": "{ans33}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following to the nearest whole number:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"numberone1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone1", "description": ""}, "money": {"definition": "random(7050..9050#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "money", "description": ""}, "total": {"definition": "({numberone1}+{numbertwo1}+{numberfour})*k", "templateType": "anything", "group": "Ungrouped variables", "name": "total", "description": ""}, "numbertwo1": {"definition": "random(2..7 except {numberone1})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo1", "description": ""}, "numberone": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone", "description": ""}, "ratioab": {"definition": "shuffle(2.1..4.4#0.1)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ratioab", "description": ""}, "ratio": {"definition": "{lent}/summ", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio", "description": ""}, "ansone": {"definition": "{ratio}*{numberone}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "anstwo": {"definition": "{ratio}*{numbertwo}", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "numberfour": {"definition": "random(2..7 except {numberone1} except {numbertwo1})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfour", "description": ""}, "ansfive": {"definition": "k*{numbertwo1}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansfive", "description": ""}, "numberthree": {"definition": "20-({numberone} + {numbertwo})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthree", "description": ""}, "anssix": {"definition": "k*{numberfour}", "templateType": "anything", "group": "Ungrouped variables", "name": "anssix", "description": ""}, "ansfour": {"definition": "k*{numberone1}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansfour", "description": ""}, "ratioc": {"definition": "10 - (ratioab[0] + ratioab[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ratioc", "description": ""}, "material": {"definition": "random('wood','timber','glass','metal','plastic')", "templateType": "anything", "group": "Ungrouped variables", "name": "material", "description": ""}, "summ": {"definition": "{numberone}+{numbertwo}+{numberthree}", "templateType": "anything", "group": "Ungrouped variables", "name": "summ", "description": ""}, "lent": {"definition": "random(140..400#20)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent", "description": ""}, "ans31": {"definition": "({money}/10)*ratioab[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "({money}/10)*ratioab[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "({money}/10)*{ratioc}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ansthree": {"definition": "{ratio}*{numberthree}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansthree", "description": ""}, "k": {"definition": "random(61..68)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "numbertwo": {"definition": "random(2..7 except {numberone})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo", "description": ""}}, "metadata": {"description": "<p>Ratio Questions</p>\n<p>rebel</p>\n<p>rebelmaths</p>\n<p></p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q3 Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["numberone", "numbertwo", "ans", "lent", "width", "area", "numberthree", "numberthreea", "numberfour", "numberfoura", "numberfive", "numberfivea", "numberfiveb", "ansone", "anstwo", "ansthree", "num1", "num2", "num3", "a1", "a2", "a3"], "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p></p>\n<p><em>Part 1:</em></p>\n<p>Add the three ratios together, which gives $15$</p>\n<p>Therefore $1$ is equal to $\\frac{180}{15}$degrees (12degrees)</p>\n<p>&nbsp;Multiply each ratio by 18 to find the value of each angle in degrees</p>\n<p>$12&nbsp;\\times \\var{num1}$</p>\n<p>$12&nbsp;\\times&nbsp;\\var{num2}$</p>\n<p>$12&nbsp;\\times&nbsp;\\var{num3}$</p>\n<p></p>\n<p><em>Part 2:</em></p>\n<p>Add the three ratios together, which gives $10$</p>\n<p>Therefore $1$ is equal to $\\frac{180}{10}$degrees (18degrees)</p>\n<p>&nbsp;Multiply each ratio by 18 to find the value of each angle in degrees</p>\n<p>$18 \\times \\var{numberthree}\\frac{1}{\\var{numberthreea}}$</p>\n<p>$18 \\times&nbsp;\\var{numberfour}\\frac{1}{\\var{numberfoura}}$</p>\n<p>$18 \\times&nbsp;\\var{numberfive}\\frac{\\var{numberfiveb}}{\\var{numberfivea}}$</p>\n<p><em></em></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>If the angles of a triangle are in the ratio $\\var{num1}:\\var{num2}:\\var{num3}$.</p>\n<p></p>\n<p>Find the angles in degrees.</p>\n<p>[[0]]degrees</p>\n<p>[[1]]degrees</p>\n<p>[[2]]degrees</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>There are 180 degrees in a triangle.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{a1}", "minValue": "{a1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a2}", "minValue": "{a2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a3}", "minValue": "{a3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>If the angles of a triangle are in the ratio $\\var{numberthree}\\frac{1}{\\var{numberthreea}}:\\var{numberfour}\\frac{1}{\\var{numberfoura}}:\\var{numberfive}\\simplify{{numberfiveb}/{numberfivea}}$.</p>\n<p></p>\n<p>Find the angles in degrees.</p>\n<p>[[0]]degrees</p>\n<p>[[1]]degrees</p>\n<p>[[2]]degrees</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Convert the fraction into top heavy fractions. Simplify this ratio into integers like in Q1 (c). Now continue as in part (a) above.</p>\n<p>Or, alternatively add the fractions in fraction form.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ansone}", "strictPrecision": false, "minValue": "{ansone}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{anstwo}", "strictPrecision": false, "minValue": "{anstwo}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ansthree}", "strictPrecision": false, "minValue": "{ansthree}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following shape questions, correct to 2 decimal places.</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "7", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "15-(num1+num2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "numberfivea": {"definition": "{numberthreea}*{numberfoura}", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfivea", "description": ""}, "ans": {"definition": "({area}-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "numberone": {"definition": "random(2..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone", "description": ""}, "anstwo": {"definition": "18*({numberfour} + (1/{numberfoura}))", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "18*({numberthree} + (1/{numberthreea}))", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "area": {"definition": "lent*width", "templateType": "anything", "group": "Ungrouped variables", "name": "area", "description": ""}, "numberfour": {"definition": "random(2..4 except {numberthree})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfour", "description": ""}, "numberthree": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthree", "description": ""}, "width": {"definition": "1-{numbertwo}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "width", "description": ""}, "numberfiveb": {"definition": "{numberfivea}-({numberthreea}+{numberfoura})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfiveb", "description": ""}, "numberthreea": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthreea", "description": ""}, "numberfoura": {"definition": "random(2..8 except {numberthreea})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfoura", "description": ""}, "a1": {"definition": "12*num1", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "12*num3", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "12*num2", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "lent": {"definition": "1+{numberone}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "lent", "description": ""}, "ansthree": {"definition": "18*({numberfive} + ({numberfiveb}/{numberfivea}))", "templateType": "anything", "group": "Ungrouped variables", "name": "ansthree", "description": ""}, "numberfive": {"definition": "random(2..4 except {numberthree} except {numberfour})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfive", "description": ""}, "numbertwo": {"definition": "random(2..25 except {numberone})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo", "description": ""}}, "metadata": {"description": "<p>Ratio Questions</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q4 Lotto Ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["number1", "number2", "number3", "number4", "prize1", "prize2", "prize3", "number5", "number6", "number7", "number8", "number9", "number10", "ans1", "ans2", "ans3", "ans4", "ans5", "ans6", "ans7", "ans8", "ans9"], "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p><em>Part 1:</em></p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times \\var{number1} \\times 1000000 = \\var{ans1}$</p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times&nbsp;\\var{number2} \\times 1000000 = \\var{ans2}$</p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times&nbsp;\\var{number3} \\times 1000000 = \\var{ans3}$</p>\n<p><em></em></p>\n<p><em>Part 2:</em></p>\n<p>$\\frac{\\var{prize2}}{\\var{number7}} \\times&nbsp;\\var{number4} = \\var{ans4}$</p>\n<p>$\\frac{\\var{prize2}}{\\var{number7}} \\times&nbsp;\\var{number5} = \\var{ans5}$</p>\n<p>$\\frac{\\var{prize2}}{\\var{number7}} \\times&nbsp;\\var{number6} = \\var{ans6}$</p>\n<p></p>\n<p><em>Part 3:</em></p>\n<p>$\\frac{\\var{prize3}}{\\var{number9}} \\times&nbsp;\\var{number8} = \\var{ans7}$</p>\n<p>$\\frac{\\var{prize3}}{\\var{number9}} \\times&nbsp;\\var{number10} = \\var{ans8}$</p>\n<p>$\\var{ans7}&nbsp;+ \\var{ans8} + \\var{prize3}&nbsp;= \\var{ans9}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Three people in a syndicate share a Lotto prize in the ratio $\\var{number1}:\\var{number2}:\\var{number3}$. If the total prize won is &euro;$\\var{prize1}$ million, how much does each person in the syndicate get?</p>\n<p><em>(Do not answer in millions)</em></p>\n<p>&euro;[[0]]</p>\n<p>&euro;[[1]]</p>\n<p>&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Hint: 1 million is 1,000,000</p>\n<p>Convert $\\var{prize1}$ million to a nice number form by multiplying by 1,000,000.</p>\n<p>We need to divide the wimmings up into smaller pieces and then share those pieces out according to the ratio. To find how many little pieces we need to make we add</p>\n<p>$\\var{number1}$ +&nbsp;$\\var{number2}$ +&nbsp;$\\var{number3}$.</p>\n<p>Divide the prize into this many pieces.</p>\n<p>Multiply by each number from the ratio to see how much each person wins.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Four people in a syndicate share a Lotto prize in the ratio $\\var{number4}:\\var{number5}:\\var{number6}:\\var{number7}$.</p>\n<p>In the recent draw, the person with the largest share won &euro;$\\var{prize2}$. How much did each of the others win?</p>\n<p>&euro;[[0]]</p>\n<p>&euro;[[1]]</p>\n<p>&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The person with the largest share got&nbsp;$\\var{number7}$ of the total&nbsp;$\\var{number4}$ +&nbsp;$\\var{number5}$ +&nbsp;$\\var{number6}$ +&nbsp;$\\var{number7}$ parts. Divide&nbsp;$\\var{prize2}$ by&nbsp;$\\var{number7}$ to see how much each part was. The first person got&nbsp;$\\var{number4}$ of these parts.</p>\n<p>How much did they get?</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "strictPrecision": false, "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans5}", "strictPrecision": false, "minValue": "{ans5}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans6}", "strictPrecision": false, "minValue": "{ans6}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>A prize fund is divided between A, B and C in the ratio $\\var{number8}:\\var{number9}:\\var{number10}$. If B's share is &euro;$\\var{prize3}$; find how much A gets, how much C gets and the total prize fund.</p>\n<p>A gets: &euro;[[0]]</p>\n<p>C gets: &euro;[[1]]</p>\n<p>Total prize fund: &euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans7}", "minValue": "{ans7}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans8}", "minValue": "{ans8}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans9}", "minValue": "{ans9}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following prize funds questions, to the nearest Euro:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "  "}, "variables": {"ans8": {"definition": "({prize3}/{number9})*{number10}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans8", "description": ""}, "ans9": {"definition": "{ans7}+{ans8}+{prize3}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans9", "description": ""}, "ans1": {"definition": "{prize1}/({number1}+{number2}+{number3}) * {number1} *1000000 ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "{prize1}/({number1}+{number2}+{number3}) * {number2} *1000000   ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "{prize1}/({number1}+{number2}+{number3}) * {number3} *1000000  ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "({prize2}/{number7}) * {number4}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans5": {"definition": "({prize2}/{number7}) * {number5}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "ans6": {"definition": "({prize2}/{number7}) * {number6}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "ans7": {"definition": "({prize3}/{number9})*{number8}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans7", "description": ""}, "prize2": {"definition": "random(29000..50000#500)*number7", "templateType": "anything", "group": "Ungrouped variables", "name": "prize2", "description": ""}, "prize3": {"definition": "random(650..950)*number9", "templateType": "anything", "group": "Ungrouped variables", "name": "prize3", "description": ""}, "prize1": {"definition": "(number1+number2+number3)* random(3.25..5.75#0.5)*0.1", "templateType": "anything", "group": "Ungrouped variables", "name": "prize1", "description": ""}, "number10": {"definition": "random(1.5..4#0.5 except {number8} except {number9})", "templateType": "anything", "group": "Ungrouped variables", "name": "number10", "description": ""}, "number6": {"definition": "random(1.5..4#0.5 except {number4} except {number5})", "templateType": "anything", "group": "Ungrouped variables", "name": "number6", "description": ""}, "number7": {"definition": "random(7..9#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number7", "description": ""}, "number4": {"definition": "random(1.5..4#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number4", "description": ""}, "number5": {"definition": "random(1.5..4#0.5 except {number4})", "templateType": "anything", "group": "Ungrouped variables", "name": "number5", "description": ""}, "number2": {"definition": "random(1.5..4.5 except {number1})", "templateType": "anything", "group": "Ungrouped variables", "name": "number2", "description": ""}, "number3": {"definition": "random(8..10)-(number1+number2)", "templateType": "anything", "group": "Ungrouped variables", "name": "number3", "description": ""}, "number1": {"definition": "random(1.5..2.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number1", "description": ""}, "number8": {"definition": "random(1.5..4#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number8", "description": ""}, "number9": {"definition": "random(1.5..4#0.5 except {number8})", "templateType": "anything", "group": "Ungrouped variables", "name": "number9", "description": ""}}, "metadata": {"description": "<p>Split winnings in a ratio</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q5 Paint and Alloy Ratio ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["material", "ratio1", "ratio2", "ratio3", "weight", "ans1", "number0", "number1", "number2", "low", "ans2", "ans3", "ans4", "place", "worker", "worker2", "worker1", "ans5", "worker3", "subvalue", "money", "ratioab", "ratioc", "ans6", "ans7", "ans8", "hcf", "ratiod", "ratiodd", "vol", "totd", "ansd1", "ansd2", "ansd3", "gla", "m"], "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p><em>Part 1:</em></p>\n<p>&nbsp;$(\\frac{\\var{weight}}{\\var{ratio3}} \\times {\\var{ratio1}}) +&nbsp;(\\frac{\\var{weight}}{\\var{ratio3}} \\times&nbsp;{\\var{ratio2}}) + \\var{weight} = \\var{ans1}$&nbsp;&nbsp;&nbsp;&nbsp;</p>\n<p><em>Part 2:</em></p>\n<p><em>Tia Maria</em></p>\n<p>$\\frac{\\var{totd}}{\\var{ratiod[0]}} \\times&nbsp;\\var{ratiod[1]} = \\var{ansd1}$</p>\n<p>Milk</p>\n<p>$\\frac{\\var{totd}}{\\var{ratiod[0]}} \\times&nbsp;\\var{ratiodd} = \\var{ansd2}$</p>\n<p>Glasses</p>\n<p>$\\frac{(\\var{totd} + \\var{ansd1} + \\var{ansd2})}{\\var{gla}}) = \\var{ansd3}$</p>\n<p><em>Part 3:</em></p>\n<p>$\\frac{\\var{vol3}}{(\\var{ratio31}+\\var{ratio32})} = &nbsp;\\var{ratioa}$</p>\n<p>$\\var{ratio31} \\times&nbsp;\\var{ratioa} = &nbsp;\\var{ans31}$</p>\n<p>$\\var{ratio32} \\times&nbsp;\\var{ratioa} = \\var{ans32}$</p>\n<p>$\\frac{\\var{vol1}}{\\var{ratio32}} \\times&nbsp;\\var{ratio31} = \\var{ans33}$</p>\n<p>$\\frac{\\var{vol2}}{\\var{ratio31}} \\times&nbsp;\\var{ratio32} = \\var{ans34}$</p>\n<p><em></em></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>An alloy consists of $\\var{material[0]}$, $\\var{material[1]}$ and&nbsp;tin in the ratio $\\var{ratio1}$:$\\var{ratio2}$:$\\var{ratio3}$. If there are $\\var{weight}$kg&nbsp;of tin in the alloy, find its total weight.</p>\n<p><em>(Answer in kg to the nearest&nbsp;whole number)</em></p>\n<p>[[0]]kg</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Have a look back at Q4 (b). This is very similar.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>A cocktail contains Vodka, Tia Maria and milk in the ratio&nbsp;$\\var{ratiod[0]}:\\var{ratiod[1]}:\\var{ratiodd}$. If $\\var{totd}$ml of Vodka is used to make this cocktail for a party, how much Tia Maria and milk is needed?</p>\n<p>Tia Maria needed =&nbsp;[[0]]ml</p>\n<p>Milk&nbsp;needed =&nbsp;[[1]]ml</p>\n<p>How many $\\var{gla}$ ml glasses will this fill?</p>\n<p><em>Count only full&nbsp;glasses!!</em></p>\n<p>[[2]]glasses</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ansd1}", "minValue": "{ansd1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ansd2}", "minValue": "{ansd2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ansd3}", "minValue": "{ansd3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Paint is made up of colours $\\var{coloura}$ and $\\var{colourb}$ in the ratio $\\var{ratio31}:\\var{ratio32}$.</p>\n<p>i) How much of each colour is in a $\\var{vol3}$ litre can of this paint (round to 2&nbsp;decimal place)?</p>\n<p>$\\var{coloura}:$ [[0]]L</p>\n<p>$\\var{colourb}:$[[1]]L</p>\n<p>ii) How much of $\\var{coloura}$ has to be added to $\\var{vol1}$ litres of $\\var{colourb}$ to make the paint?</p>\n<p><em>(Round to 2 decimal places)</em></p>\n<p><em>(Remember to use units, i.e. L for litres)</em></p>\n<p>$\\var{coloura}:$[[2]]L</p>\n<p>iii) How much of $\\var{colourb}$ has to be added to $\\var{vol2}$ litres of $\\var{coloura}$ to make the paint?</p>\n<p><em>(Round to 2 decimal places)</em></p>\n<p><em>$\\var{colourb}:$[[3]]L</em></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "strictPrecision": false, "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "strictPrecision": false, "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}", "strictPrecision": false, "minValue": "{ans33}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans34}", "strictPrecision": false, "minValue": "{ans34}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following ratio questions:</p>", "variable_groups": [{"variables": ["coloura", "colourb", "ratio31", "ratio32", "vol3", "vol1", "vol2", "ratioa", "ans31", "ans32", "ans33", "ans34"], "name": "Unnamed group"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans8": {"definition": "({money}/10)*{ratioc}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans8", "description": ""}, "ratio32": {"definition": "random(2..6#2)", "templateType": "anything", "group": "Unnamed group", "name": "ratio32", "description": ""}, "weight": {"definition": "{ratio3}*m", "templateType": "anything", "group": "Ungrouped variables", "name": "weight", "description": ""}, "vol": {"definition": "random(20..26)", "templateType": "anything", "group": "Ungrouped variables", "name": "vol", "description": ""}, "money": {"definition": "random(7050..9050#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "money", "description": ""}, "ans2": {"definition": "({low}/number0)*1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "({low}/number1)*5", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "({low}/number2)*7", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans5": {"definition": "({worker3}/worker[2]) + {subvalue} + {worker3}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "ans6": {"definition": "({money}/10)*ratioab[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "ans7": {"definition": "({money}/10)*ratioab[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans7", "description": ""}, "ratio1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio1", "description": ""}, "ratio3": {"definition": "random(1..9 except {ratio1} except {ratio2})", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio3", "description": ""}, "ratio2": {"definition": "random(1..9 except {ratio1})", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio2", "description": ""}, "colourb": {"definition": "random('brown','yellow','white','grey','maroon') ", "templateType": "anything", "group": "Unnamed group", "name": "colourb", "description": ""}, "coloura": {"definition": "random('red','black','pink','blue','green','purple')", "templateType": "anything", "group": "Unnamed group", "name": "coloura", "description": ""}, "ratioab": {"definition": "shuffle(2.1..4.4#0.1)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ratioab", "description": ""}, "ratio31": {"definition": "random(1..7#2)", "templateType": "anything", "group": "Unnamed group", "name": "ratio31", "description": ""}, "totd": {"definition": "vol*ratiod[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "totd", "description": ""}, "subvalue": {"definition": "(({worker3}/worker[2])/worker[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "subvalue", "description": ""}, "hcf": {"definition": "gcd(4,12)", "templateType": "anything", "group": "Ungrouped variables", "name": "hcf", "description": ""}, "low": {"definition": "lcm([number0,number1,number2])", "templateType": "anything", "group": "Ungrouped variables", "name": "low", "description": ""}, "ans1": {"definition": " (({weight}/{ratio3})*{ratio1}) + (({weight}/{ratio3})*{ratio2}) + {weight}      ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ansd1": {"definition": "vol*ratiod[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ansd1", "description": ""}, "ansd3": {"definition": "floor((totd+ansd1+ansd2)/gla)", "templateType": "anything", "group": "Ungrouped variables", "name": "ansd3", "description": ""}, "ansd2": {"definition": "vol*ratiodd", "templateType": "anything", "group": "Ungrouped variables", "name": "ansd2", "description": ""}, "ratiod": {"definition": "shuffle(2..7)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ratiod", "description": ""}, "ratioa": {"definition": "{vol3}/({ratio31}+{ratio32})", "templateType": "anything", "group": "Unnamed group", "name": "ratioa", "description": ""}, "ratioc": {"definition": "10 - (ratioab[0] + ratioab[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ratioc", "description": ""}, "material": {"definition": "shuffle(['manganese','silicon','copper','zinc','iron','cobalt','platinum'])[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "material", "description": ""}, "worker": {"definition": "shuffle(5..12)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker", "description": ""}, "number2": {"definition": "random(10,13,15,16)", "templateType": "anything", "group": "Ungrouped variables", "name": "number2", "description": ""}, "number0": {"definition": "random(2,3,4,6)", "templateType": "anything", "group": "Ungrouped variables", "name": "number0", "description": ""}, "vol2": {"definition": "random(0.5..1.5#0.5 except{vol3})", "templateType": "anything", "group": "Unnamed group", "name": "vol2", "description": ""}, "ans31": {"definition": "{ratio31}*{ratioa}", "templateType": "anything", "group": "Unnamed group", "name": "ans31", "description": ""}, "ans32": {"definition": "{ratio32}*{ratioa}", "templateType": "anything", "group": "Unnamed group", "name": "ans32", "description": ""}, "ans33": {"definition": "({vol1}/{ratio32}) * {ratio31}", "templateType": "anything", "group": "Unnamed group", "name": "ans33", "description": ""}, "ans34": {"definition": "({vol2}/{ratio31}) * {ratio32}", "templateType": "anything", "group": "Unnamed group", "name": "ans34", "description": ""}, "vol3": {"definition": "random(2,2.5,5,8,10,15,20)", "templateType": "anything", "group": "Unnamed group", "name": "vol3", "description": ""}, "worker1": {"definition": "worker[0] * worker[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker1", "description": ""}, "gla": {"definition": "random(35..60#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "gla", "description": ""}, "worker3": {"definition": "{worker2} * worker[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker3", "description": ""}, "worker2": {"definition": "{worker1} * worker[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker2", "description": ""}, "m": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "number1": {"definition": "random(8,9,11,12)", "templateType": "anything", "group": "Ungrouped variables", "name": "number1", "description": ""}, "place": {"definition": "random('shop','business','factory')", "templateType": "anything", "group": "Ungrouped variables", "name": "place", "description": ""}, "ratiodd": {"definition": "15 - (ratiod[0]+ratiod[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ratiodd", "description": ""}, "vol1": {"definition": "random(10..25 except{vol3})", "templateType": "anything", "group": "Unnamed group", "name": "vol1", "description": ""}}, "metadata": {"description": "<p>Ratios used in alloys and mixing paints</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q6 Ratio with rectangles ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["numberone", "numbertwo", "ans", "lent", "width", "area", "numberthree", "numberthreea", "numberfour", "numberfoura", "numberfive", "numberfivea", "numberfiveb", "ansone", "anstwo", "ansthree", "num1", "num2", "num3", "a1", "a2", "a3"], "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p></p>\n<p><em>Part 1:</em></p>\n<p>If the length is increased by $\\var{numberone}$%, the length becomes $\\var{lent}$</p>\n<p>Similiarly with the width,</p>\n<p>If the width is decreased by $\\var{numbertwo}$%, the width becomes $\\var{width}$</p>\n<p>multiply length by width to get area:</p>\n<p>$\\var{lent}&nbsp;\\times \\var{width} = \\var{area}$</p>\n<p>Then, multiply the area by 100 to get it as a percentage</p>\n<p>To see if it is a decrease or increase, take away 100 from it</p>\n<p>If it is a negative number it is a decrease, and if a positive number it increases.</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>The sides of a rectangle are altered. The length is increased by $\\var{numberone}$% while the width is decreased by $\\var{numbertwo}$%. Find the precentage change in the area of the rectangle stating whether it is an increase or a decrease, by indicating a decrease with a negative sign.</p>\n<p><em>(e.g. -8% shows an 8% decrease, and 8%&nbsp;shows an 8% increase)</em></p>\n<p><em>[[0]]%</em></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Imagine the rectangle started off with length 1m and width 1m. In that case what would the new length and width be equal to. The area of a rectangle is length by width. Is this less than or equal to 1 square metre? By how much?</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans}", "strictPrecision": false, "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following shape questions, correct to 2 decimal places.</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num1": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "7", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "15-(num1+num2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "numberfivea": {"definition": "{numberthreea}*{numberfoura}", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfivea", "description": ""}, "ans": {"definition": "({area}-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "numberone": {"definition": "random(2..25)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone", "description": ""}, "anstwo": {"definition": "18*({numberfour} + (1/{numberfoura}))", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo", "description": ""}, "ansone": {"definition": "18*({numberthree} + (1/{numberthreea}))", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone", "description": ""}, "area": {"definition": "lent*width", "templateType": "anything", "group": "Ungrouped variables", "name": "area", "description": ""}, "numberfour": {"definition": "random(2..4 except {numberthree})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfour", "description": ""}, "numberthree": {"definition": "random(2..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthree", "description": ""}, "width": {"definition": "1-{numbertwo}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "width", "description": ""}, "numberfiveb": {"definition": "{numberfivea}-({numberthreea}+{numberfoura})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfiveb", "description": ""}, "numberthreea": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthreea", "description": ""}, "numberfoura": {"definition": "random(2..8 except {numberthreea})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfoura", "description": ""}, "a1": {"definition": "12*num1", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "12*num3", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "12*num2", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "lent": {"definition": "1+{numberone}/100", "templateType": "anything", "group": "Ungrouped variables", "name": "lent", "description": ""}, "ansthree": {"definition": "18*({numberfive} + ({numberfiveb}/{numberfivea}))", "templateType": "anything", "group": "Ungrouped variables", "name": "ansthree", "description": ""}, "numberfive": {"definition": "random(2..4 except {numberthree} except {numberfour})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfive", "description": ""}, "numbertwo": {"definition": "random(2..25 except {numberone})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo", "description": ""}}, "metadata": {"description": "<p>Ratio of sides of rectangles</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q7 Ratio work times", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {"": {"definition": "", "type": "number", "language": "jme", "parameters": []}}, "ungrouped_variables": ["number1", "number2", "time1", "time2", "timeword1", "timeword2", "ans1", "ans2", "number3", "ans3", "place", "worker", "worker2", "worker1", "worker3", "ans11", "subvalue"], "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p><em>Part 1:</em></p>\n<p>Unskilled workers: $\\var{worker3}$</p>\n<p>Skilled workers: $\\frac{\\var{worker3}}{\\var{worker[2]}} = \\var{worker2}$</p>\n<p>Foremen: $\\frac{\\var{worker2}}{\\var{worker[1]}} = \\var{subvalue}$</p>\n<p>Total: $\\var{worker3} + \\var{worker2} + \\var{subvalue} = \\var{ans5}$</p>\n<p><em></em></p>\n<p><em>Part 2:</em></p>\n<p>$\\frac{(\\var{number1} \\times \\var{time1})}{\\var{number2}} = \\var{ans1}$</p>\n<p></p>\n<p><em>Part 3:</em></p>\n<p>$\\frac{(\\var{number1} \\times&nbsp;\\var{time1}\\times \\var{time1})}{\\var{number2}} = \\var{ans2}$</p>\n<p>$\\frac{(\\var{number1} \\times&nbsp;\\var{time1}\\times \\var{time1})}{\\var{number3}} = \\var{ans3}$</p>\n<p></p>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>A $\\var{place}$ employs $\\var{worker3}$ unskilled workers, one skilled worker for every $\\var{worker[2]}$ unskilled workers&nbsp;and one foreman for every $\\var{worker[1]}$ skilled workers. How many people are employed in this $\\var{place}$?</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Write the information out as one ratio. Divide the employees in this ratio.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "strictPrecision": false, "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "0", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>If $\\var{number1}$ people can complete a task in $\\var{time1}$ hours, how long would it take $\\var{number2}$ people to complete the same task, assuming the work rate remains constant?</p>\n<p>[[0]]hours</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>It takes $\\var{number1} \\times \\var{time1}$ man hours to complete the task. Divide that by&nbsp;$\\var{number2}$ to find out how long it takes now.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>It takes $\\var{number1}$ people $\\var{time1}$ days&nbsp;to do a job. If they work $\\var{time2}$ hours per day, how long would it take:</p>\n<p>i) $\\var{number2}$ people to do the same job?&nbsp;</p>\n<p>[[0]]hours</p>\n<p>ii) $\\var{number3}$ people to do the same job?&nbsp;</p>\n<p>[[1]]hours</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the&nbsp;following questions, to 2 decimal places. &nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"timeword1": {"definition": "random(['hours','days'])", "templateType": "anything", "group": "Ungrouped variables", "name": "timeword1", "description": ""}, "timeword2": {"definition": "random(['hours','days'] except {timeword1})", "templateType": "anything", "group": "Ungrouped variables", "name": "timeword2", "description": ""}, "worker2": {"definition": "{worker1} * worker[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker2", "description": ""}, "worker1": {"definition": "worker[0] * worker[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker1", "description": ""}, "ans1": {"definition": "({number1}*{time1})/{number2}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "({number1}*{time1}*{time2})/{number2}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "({number1}*{time1}*{time2})/{number3}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "worker": {"definition": "shuffle(5..12)[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker", "description": ""}, "time1": {"definition": "random(5..20 except {number1} except {number2})", "templateType": "anything", "group": "Ungrouped variables", "name": "time1", "description": ""}, "time2": {"definition": "random(5..10#0.5 except {number1} except {number1} except {time1})", "templateType": "anything", "group": "Ungrouped variables", "name": "time2", "description": ""}, "subvalue": {"definition": "(({worker3}/worker[2])/worker[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "subvalue", "description": ""}, "ans11": {"definition": "({worker3}/worker[2]) + {subvalue} + {worker3}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "number2": {"definition": "random(3..18 except {number1})", "templateType": "anything", "group": "Ungrouped variables", "name": "number2", "description": ""}, "number3": {"definition": "random(3..18 except {number1} except {number2})", "templateType": "anything", "group": "Ungrouped variables", "name": "number3", "description": ""}, "number1": {"definition": "random(5..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "number1", "description": ""}, "place": {"definition": "random('shop','business','factory')", "templateType": "anything", "group": "Ungrouped variables", "name": "place", "description": ""}, "worker3": {"definition": "{worker2} * worker[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "worker3", "description": ""}}, "metadata": {"description": "<p>Ratio, working hours</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}], "contributors": [{"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "extensions": [], "custom_part_types": [], "resources": []}