// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Q2 Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "", "variable_groups": [], "preamble": {"js": "", "css": ""}, "extensions": [], "rulesets": {}, "variables": {"numbertwo1": {"description": "", "group": "Ungrouped variables", "definition": "random(2..7 except {numberone1})", "name": "numbertwo1", "templateType": "anything"}, "ansfour": {"description": "", "group": "Ungrouped variables", "definition": "k*{numberone1}", "name": "ansfour", "templateType": "anything"}, "money": {"description": "", "group": "Ungrouped variables", "definition": "random(7050..9050#100)", "name": "money", "templateType": "anything"}, "anssix": {"description": "", "group": "Ungrouped variables", "definition": "k*{numberfour}", "name": "anssix", "templateType": "anything"}, "ans33": {"description": "", "group": "Ungrouped variables", "definition": "({money}/(ratioab[0]+ratioab[1]+ratioc))*{ratioc}", "name": "ans33", "templateType": "anything"}, "total": {"description": "", "group": "Ungrouped variables", "definition": "({numberone1}+{numbertwo1}+{numberfour})*k", "name": "total", "templateType": "anything"}, "numbertwo": {"description": "", "group": "Ungrouped variables", "definition": "random(2..7 except {numberone})", "name": "numbertwo", "templateType": "anything"}, "ratio": {"description": "", "group": "Ungrouped variables", "definition": "{lent}/summ", "name": "ratio", "templateType": "anything"}, "k": {"description": "", "group": "Ungrouped variables", "definition": "random(61..68)", "name": "k", "templateType": "anything"}, "ans32": {"description": "", "group": "Ungrouped variables", "definition": "({money}/(ratioab[0]+ratioab[1]+ratioc))*ratioab[1]", "name": "ans32", "templateType": "anything"}, "material": {"description": "", "group": "Ungrouped variables", "definition": "random('wood','timber','glass','metal','plastic')", "name": "material", "templateType": "anything"}, "ratioab": {"description": "", "group": "Ungrouped variables", "definition": "shuffle(1.2..4.8#0.2)[0..2]", "name": "ratioab", "templateType": "anything"}, "ans31": {"description": "", "group": "Ungrouped variables", "definition": "({money}/(ratioab[0]+ratioab[1]+ratioc))*ratioab[0]", "name": "ans31", "templateType": "anything"}, "ratioc": {"description": "", "group": "Ungrouped variables", "definition": "5*2^random(1..3) - (ratioab[0] + ratioab[1])", "name": "ratioc", "templateType": "anything"}, "anstwo": {"description": "", "group": "Ungrouped variables", "definition": "{ratio}*{numbertwo}", "name": "anstwo", "templateType": "anything"}, "lent": {"description": "", "group": "Ungrouped variables", "definition": "random(140..400#20)", "name": "lent", "templateType": "anything"}, "ansone": {"description": "", "group": "Ungrouped variables", "definition": "{ratio}*{numberone}", "name": "ansone", "templateType": "anything"}, "numberone1": {"description": "", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "numberone1", "templateType": "anything"}, "summ": {"description": "", "group": "Ungrouped variables", "definition": "{numberone}+{numbertwo}+{numberthree}", "name": "summ", "templateType": "anything"}, "numberfour": {"description": "", "group": "Ungrouped variables", "definition": "random(2..7 except {numberone1} except {numbertwo1})", "name": "numberfour", "templateType": "anything"}, "numberone": {"description": "", "group": "Ungrouped variables", "definition": "random(2..9)", "name": "numberone", "templateType": "anything"}, "ansthree": {"description": "", "group": "Ungrouped variables", "definition": "{ratio}*{numberthree}", "name": "ansthree", "templateType": "anything"}, "numberthree": {"description": "", "group": "Ungrouped variables", "definition": "20-({numberone} + {numbertwo})", "name": "numberthree", "templateType": "anything"}, "ansfive": {"description": "", "group": "Ungrouped variables", "definition": "k*{numbertwo1}", "name": "ansfive", "templateType": "anything"}}, "tags": [], "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Ratio Questions</p>\n<p>rebel</p>\n<p>rebelmaths</p>\n<p></p>"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "<p><strong>(a)</strong></p>\n<p>Add the ratio numbers to get&nbsp;$\\var{numberone}+\\var{numbertwo}+\\var{numberthree}=\\var{summ}$</p>\n<p>Now divide the total length by this to work out the value of one part:</p>\n<p><span class=\"re2\">$\\frac{\\var{lent}}{\\var{summ}}=\\var{lent/summ}$</span></p>\n<p><span class=\"sy0\">Now&nbsp;multiply&nbsp;this by each number in the ratio to give:</span></p>\n<p><span class=\"sy0\">$\\var{numberone} \\times \\var{ratio} =\\var{numberone*ratio}$</span></p>\n<p><span class=\"sy0\">$\\var{numbertwo} \\times&nbsp;\\var{ratio}= \\var{numbertwo*ratio}$</span></p>\n<p><span class=\"sy0\">$\\var{numberthree} \\times&nbsp;\\var{ratio}=\\var{numberthree*ratio}$</span></p>\n<p><span class=\"sy0\"></span></p>\n<p><strong><span class=\"sy0\">(b)</span></strong></p>\n<p><span class=\"sy0\">Use the same method as in part (i)</span></p>\n<p><span class=\"sy0\">$\\frac{\\var{total}}{(\\var{numberone1}+\\var{numbertwo1}+\\var{numberfour})}=\\var{k}$</span></p>\n<p><span class=\"sy0\">$\\var{numberone} \\times \\var{k}=\\var{numberone*k}$</span></p>\n<p><span class=\"sy0\">$\\var{numbertwo} \\times \\var{k}=\\var{numbertwo*k}$</span></p>\n<p><span class=\"sy0\">$\\var{numberfour} \\times \\var{k}=\\var{numberthree*k}$</span></p>\n<p><span class=\"sy0\"></span></p>\n<p><strong>(c)</strong></p>\n<p>$\\var{ratioab[0]} + \\var{ratioab[1]} + \\var{ratioc}=\\var{ratioab[0]+ratioab[1]+ratioc}$</p>\n<p>$\\frac{\\var{money}}{\\var{ratioab[0]+ratioab[1]+ratioc}}=\\var{money/(ratioab[0]+ratioab[1]+ratioc)}$</p>\n<p>$\\var{money/(ratioab[0]+ratioab[1]+ratioc)}&nbsp;\\times&nbsp;\\var{ratioab[0]} = &pound;\\var{dpformat(ans31,2)}$</p>\n<p>$\\var{money/(ratioab[0]+ratioab[1]+ratioc)}&nbsp;\\times&nbsp;\\var{ratioab[1]} = &pound;\\var{dpformat(ans32,2)}$</p>\n<p>$\\var{money/(ratioab[0]+ratioab[1]+ratioc)}&nbsp;\\times&nbsp;\\var{ratioc}&nbsp;= &pound;\\var{dpformat(ans33,2)}$</p>", "name": "Simon's copy of Q2 Ratios", "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"], "parts": [{"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "sortAnswers": false, "steps": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "scripts": {}, "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 this 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": [], "extendBaseMarkingAlgorithm": true, "type": "information", "customMarkingAlgorithm": "", "marks": 0}], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "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>", "stepsPenalty": 0, "gaps": [{"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{ansone}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "{ansone}", "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{anstwo}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "{anstwo}", "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{ansthree}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "{ansthree}", "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": ""}, {"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "sortAnswers": false, "steps": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "scripts": {}, "prompt": "<p>To double check your final answer, add&nbsp;your final results together. You should get&nbsp;$\\var{total}$.</p>", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "information", "customMarkingAlgorithm": "", "marks": 0}], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "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>", "stepsPenalty": 0, "gaps": [{"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{ansfour}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "{ansfour}", "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{ansfive}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "{ansfive}", "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}, {"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{anssix}", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "minValue": "{anssix}", "marks": 1, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": ""}, {"showFeedbackIcon": true, "unitTests": [], "scripts": {}, "sortAnswers": false, "steps": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "unitTests": [], "scripts": {}, "prompt": "<p>Just as before, add all parts together and divide by this.</p>", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "information", "customMarkingAlgorithm": "", "marks": 0}], "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<p>Divide &pound;$\\var{money}$ in the ratio $\\var{ratioab[0]}:\\var{ratioab[1]}:\\var{ratioc}$</p>\n<p><em>(Give answers correct to 2&nbsp;decimal places)</em></p>\n<p>&pound;[[0]] : &pound;[[1]] : &pound;[[2]]</p>", "stepsPenalty": 0, "gaps": [{"maxValue": "{ans31}", "precision": "2", "scripts": {}, "precisionType": "dp", "mustBeReducedPC": 0, "variableReplacements": [], "minValue": "{ans31}", "unitTests": [], "allowFractions": false, "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "mustBeReduced": false, "precisionPartialCredit": 0, "extendBaseMarkingAlgorithm": true, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "strictPrecision": false, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}, {"maxValue": "{ans32}", "precision": "2", "scripts": {}, "precisionType": "dp", "mustBeReducedPC": 0, "variableReplacements": [], "minValue": "{ans32}", "unitTests": [], "allowFractions": false, "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "mustBeReduced": false, "precisionPartialCredit": 0, "extendBaseMarkingAlgorithm": true, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "strictPrecision": false, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}, {"maxValue": "{ans33}", "precision": "2", "scripts": {}, "precisionType": "dp", "mustBeReducedPC": 0, "variableReplacements": [], "minValue": "{ans33}", "unitTests": [], "allowFractions": false, "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "type": "numberentry", "showFeedbackIcon": true, "mustBeReduced": false, "precisionPartialCredit": 0, "extendBaseMarkingAlgorithm": true, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "strictPrecision": false, "correctAnswerFraction": false, "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": ""}], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}