// Numbas version: exam_results_page_options
{"name": "Ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"scripts": {}, "variableReplacements": [], "steps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "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>", "scripts": {}, "type": "information"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "stepsPenalty": 0, "showFeedbackIcon": true, "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": [{"correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ansone}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "{ansone}", "mustBeReduced": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "precisionPartialCredit": 0, "showFeedbackIcon": true, "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "precision": "2"}, {"correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{anstwo}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "{anstwo}", "mustBeReduced": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "precisionPartialCredit": 0, "showFeedbackIcon": true, "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "precision": "2"}, {"correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ansthree}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "{ansthree}", "mustBeReduced": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "precisionPartialCredit": 0, "showFeedbackIcon": true, "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "precision": "2"}]}, {"scripts": {}, "variableReplacements": [], "steps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "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>", "scripts": {}, "type": "information"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "stepsPenalty": 0, "showFeedbackIcon": true, "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": [{"correctAnswerStyle": "plain", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ansfour}", "showFeedbackIcon": true, "showCorrectAnswer": true, "minValue": "{ansfour}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false}, {"correctAnswerStyle": "plain", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ansfive}", "showFeedbackIcon": true, "showCorrectAnswer": true, "minValue": "{ansfive}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false}, {"correctAnswerStyle": "plain", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{anssix}", "showFeedbackIcon": true, "showCorrectAnswer": true, "minValue": "{anssix}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "scripts": {}, "allowFractions": false}]}, {"scripts": {}, "variableReplacements": [], "steps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "prompt": "<p>Just as before, add all parts together and divide by this.</p>", "scripts": {}, "type": "information"}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "stepsPenalty": 0, "showFeedbackIcon": true, "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": [{"correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ans31}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "{ans31}", "mustBeReduced": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "precisionPartialCredit": 0, "showFeedbackIcon": true, "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "precision": "2"}, {"correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ans32}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "{ans32}", "mustBeReduced": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "precisionPartialCredit": 0, "showFeedbackIcon": true, "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "precision": "2"}, {"correctAnswerStyle": "plain", "type": "numberentry", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{ans33}", "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "showCorrectAnswer": true, "correctAnswerFraction": false, "minValue": "{ans33}", "mustBeReduced": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "precisionPartialCredit": 0, "showFeedbackIcon": true, "scripts": {}, "mustBeReducedPC": 0, "strictPrecision": false, "precision": "2"}]}], "variables": {"ansfour": {"group": "Ungrouped variables", "name": "ansfour", "templateType": "anything", "description": "", "definition": "k*{numberone1}"}, "numbertwo": {"group": "Ungrouped variables", "name": "numbertwo", "templateType": "anything", "description": "", "definition": "random(2..7 except {numberone})"}, "ratioc": {"group": "Ungrouped variables", "name": "ratioc", "templateType": "anything", "description": "", "definition": "10 - (ratioab[0] + ratioab[1])"}, "ratio": {"group": "Ungrouped variables", "name": "ratio", "templateType": "anything", "description": "", "definition": "{lent}/summ"}, "ans32": {"group": "Ungrouped variables", "name": "ans32", "templateType": "anything", "description": "", "definition": "({money}/10)*ratioab[1]"}, "numberfour": {"group": "Ungrouped variables", "name": "numberfour", "templateType": "anything", "description": "", "definition": "random(2..7 except {numberone1} except {numbertwo1})"}, "ratioab": {"group": "Ungrouped variables", "name": "ratioab", "templateType": "anything", "description": "", "definition": "shuffle(2.1..4.4#0.1)[0..2]"}, "ans31": {"group": "Ungrouped variables", "name": "ans31", "templateType": "anything", "description": "", "definition": "({money}/10)*ratioab[0]"}, "numbertwo1": {"group": "Ungrouped variables", "name": "numbertwo1", "templateType": "anything", "description": "", "definition": "random(2..7 except {numberone1})"}, "numberone1": {"group": "Ungrouped variables", "name": "numberone1", "templateType": "anything", "description": "", "definition": "random(2..9)"}, "ansthree": {"group": "Ungrouped variables", "name": "ansthree", "templateType": "anything", "description": "", "definition": "{ratio}*{numberthree}"}, "ansone": {"group": "Ungrouped variables", "name": "ansone", "templateType": "anything", "description": "", "definition": "{ratio}*{numberone}"}, "material": {"group": "Ungrouped variables", "name": "material", "templateType": "anything", "description": "", "definition": "random('wood','timber','glass','metal','plastic')"}, "anstwo": {"group": "Ungrouped variables", "name": "anstwo", "templateType": "anything", "description": "", "definition": "{ratio}*{numbertwo}"}, "numberthree": {"group": "Ungrouped variables", "name": "numberthree", "templateType": "anything", "description": "", "definition": "20-({numberone} + {numbertwo})"}, "money": {"group": "Ungrouped variables", "name": "money", "templateType": "anything", "description": "", "definition": "random(7050..9050#100)"}, "numberone": {"group": "Ungrouped variables", "name": "numberone", "templateType": "anything", "description": "", "definition": "random(2..9)"}, "ansfive": {"group": "Ungrouped variables", "name": "ansfive", "templateType": "anything", "description": "", "definition": "k*{numbertwo1}"}, "anssix": {"group": "Ungrouped variables", "name": "anssix", "templateType": "anything", "description": "", "definition": "k*{numberfour}"}, "ans33": {"group": "Ungrouped variables", "name": "ans33", "templateType": "anything", "description": "", "definition": "({money}/10)*{ratioc}"}, "summ": {"group": "Ungrouped variables", "name": "summ", "templateType": "anything", "description": "", "definition": "{numberone}+{numbertwo}+{numberthree}"}, "lent": {"group": "Ungrouped variables", "name": "lent", "templateType": "anything", "description": "", "definition": "random(140..400#20)"}, "k": {"group": "Ungrouped variables", "name": "k", "templateType": "anything", "description": "", "definition": "random(61..68)"}, "total": {"group": "Ungrouped variables", "name": "total", "templateType": "anything", "description": "", "definition": "({numberone1}+{numbertwo1}+{numberfour})*k"}}, "functions": {}, "tags": [], "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"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Ratio Questions</p>"}, "extensions": [], "statement": "<h2>Solve the following to the nearest whole number:</h2>", "rulesets": {}, "preamble": {"js": "", "css": ""}, "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>", "name": "Ratios", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}