// Numbas version: exam_results_page_options
{"navigation": {"showfrontpage": true, "preventleave": true, "onleave": {"message": "", "action": "none"}, "browse": true, "reverse": true, "allowregen": true, "showresultspage": "oncompletion"}, "timing": {"allowPause": true, "timeout": {"message": "", "action": "none"}, "timedwarning": {"message": "", "action": "none"}}, "percentPass": 0, "duration": 0, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "Simple ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}], "functions": {}, "ungrouped_variables": ["this", "whichone", "u", "t", "y", "x"], "tags": [], "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "advice": "<p>The ratio of ingredients $X$ and $Y$ is $\\var{x}: \\var{y}$.</p>\n<p>This means that for every $\\var{x}$g of $X$, we need $\\var{y}$g of $Y$. You could imagine organising your ingredients so that you put ingredient $X$ into small bags containing&nbsp;$\\var{x}$g and ingredient $Y$ into small bags containing&nbsp;$\\var{y}$g.</p>\n<p>For each 'batch' of cake mixture you will need one bag of each of the secret ingredients, which will weigh a total of $ \\simplify { {x} + {y} }$g in total.</p>\n<p>For a total of $ \\simplify{{t} *({x}+{y})}$g of secret ingredients we will need $\\var{t}$ batches.</p>\n<p>This means we will need $ \\var{t} \\times \\var{whichone}=\\var{t*whichone} $g of ingredient {this}.</p>", "rulesets": {}, "parts": [{"prompt": "<p>A cake recipe includes two secret ingredients $X$ and $Y$. These must be added so that the ratio $ X:Y $ is $\\var{x}:\\var{y}$.</p>\n<p>The combined weight of the two secret ingredients is $ \\simplify{{t}*({x}+{y})}$g.</p>\n<p>How much of ingredient {this} should be added?</p>\n<p>[[0]]g</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "t*whichone", "minValue": "t*whichone", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "showPrecisionHint": false, "type": "numberentry"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>Solve the following ratio problem.</p>", "type": "question", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"this": {"definition": "if(u=0,'$X$',\"$Y$\")", "templateType": "anything", "group": "Ungrouped variables", "name": "this", "description": ""}, "whichone": {"definition": "if(u=0,x,y)", "templateType": "anything", "group": "Ungrouped variables", "name": "whichone", "description": ""}, "u": {"definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(3..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "y": {"definition": "random(5,7,11,13)", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(2,4,6,8)", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}}, "showQuestionGroupNames": false, "metadata": {"description": "<p>Given the ratio of ingredients and the total amount of ingredients work out how much of one of the ingredients is needed.</p>", "licence": "Creative Commons Attribution 4.0 International"}}, {"name": "Ratios L1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}], "rulesets": {}, "preamble": {"css": "", "js": ""}, "parts": [{"type": "gapfill", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "stepsPenalty": 0, "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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>", "gaps": [{"strictPrecision": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ansone}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ansone}", "precision": "2", "variableReplacements": [], "scripts": {}}, {"strictPrecision": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{anstwo}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{anstwo}", "precision": "2", "variableReplacements": [], "scripts": {}}, {"strictPrecision": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ansthree}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ansthree}", "precision": "2", "variableReplacements": [], "scripts": {}}], "variableReplacements": [], "steps": [{"type": "information", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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": []}]}, {"type": "gapfill", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "stepsPenalty": 0, "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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>", "gaps": [{"showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ansfour}", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ansfour}", "variableReplacements": [], "scripts": {}}, {"showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ansfive}", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ansfive}", "variableReplacements": [], "scripts": {}}, {"showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{anssix}", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{anssix}", "variableReplacements": [], "scripts": {}}], "variableReplacements": [], "steps": [{"type": "information", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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": []}]}, {"type": "gapfill", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "stepsPenalty": 0, "scripts": {}, "marks": 0, "showCorrectAnswer": true, "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>", "gaps": [{"strictPrecision": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ans31}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ans31}", "precision": "2", "variableReplacements": [], "scripts": {}}, {"strictPrecision": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ans32}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ans32}", "precision": "2", "variableReplacements": [], "scripts": {}}, {"strictPrecision": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{ans33}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "type": "numberentry", "showPrecisionHint": false, "mustBeReduced": false, "correctAnswerFraction": false, "marks": 1, "allowFractions": false, "minValue": "{ans33}", "precision": "2", "variableReplacements": [], "scripts": {}}], "variableReplacements": [], "steps": [{"type": "information", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>Just as before, add all parts together and divide by this.</p>", "variableReplacements": []}]}], "metadata": {"description": "<p>Ratio Questions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "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"], "variables": {"ansfive": {"description": "", "definition": "k*{numbertwo1}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansfive"}, "ansthree": {"description": "", "definition": "{ratio}*{numberthree}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansthree"}, "numberone1": {"description": "", "definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone1"}, "ans32": {"description": "", "definition": "({money}/10)*ratioab[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32"}, "ratioab": {"description": "", "definition": "shuffle(2.1..4.4#0.1)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ratioab"}, "anstwo": {"description": "", "definition": "{ratio}*{numbertwo}", "templateType": "anything", "group": "Ungrouped variables", "name": "anstwo"}, "ratio": {"description": "", "definition": "{lent}/summ", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio"}, "anssix": {"description": "", "definition": "k*{numberfour}", "templateType": "anything", "group": "Ungrouped variables", "name": "anssix"}, "numbertwo1": {"description": "", "definition": "random(2..7 except {numberone1})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo1"}, "ansfour": {"description": "", "definition": "k*{numberone1}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansfour"}, "ratioc": {"description": "", "definition": "10 - (ratioab[0] + ratioab[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ratioc"}, "material": {"description": "", "definition": "random('wood','timber','glass','metal','plastic')", "templateType": "anything", "group": "Ungrouped variables", "name": "material"}, "k": {"description": "", "definition": "random(61..68)", "templateType": "anything", "group": "Ungrouped variables", "name": "k"}, "numberfour": {"description": "", "definition": "random(2..7 except {numberone1} except {numbertwo1})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberfour"}, "numbertwo": {"description": "", "definition": "random(2..7 except {numberone})", "templateType": "anything", "group": "Ungrouped variables", "name": "numbertwo"}, "ans31": {"description": "", "definition": "({money}/10)*ratioab[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31"}, "money": {"description": "", "definition": "random(7050..9050#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "money"}, "numberthree": {"description": "", "definition": "20-({numberone} + {numbertwo})", "templateType": "anything", "group": "Ungrouped variables", "name": "numberthree"}, "ansone": {"description": "", "definition": "{ratio}*{numberone}", "templateType": "anything", "group": "Ungrouped variables", "name": "ansone"}, "summ": {"description": "", "definition": "{numberone}+{numbertwo}+{numberthree}", "templateType": "anything", "group": "Ungrouped variables", "name": "summ"}, "ans33": {"description": "", "definition": "({money}/10)*{ratioc}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33"}, "lent": {"description": "", "definition": "random(140..400#20)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent"}, "numberone": {"description": "", "definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "numberone"}, "total": {"description": "", "definition": "({numberone1}+{numbertwo1}+{numberfour})*k", "templateType": "anything", "group": "Ungrouped variables", "name": "total"}}, "functions": {}, "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>", "tags": [], "statement": "<h2>Solve the following to the nearest whole number:</h2>", "type": "question"}]}], "feedback": {"advicethreshold": 0, "allowrevealanswer": true, "showanswerstate": true, "showactualmark": true, "intro": "", "showtotalmark": true, "feedbackmessages": []}, "showQuestionGroupNames": false, "showstudentname": true, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "name": "Ratios", "type": "exam", "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}], "extensions": [], "custom_part_types": [], "resources": []}