// Numbas version: finer_feedback_settings
{"name": "Q2 Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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"], "name": "Q2 Ratios", "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"}], "extensions": [], "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": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}