// Numbas version: exam_results_page_options
{"name": "Kinga's copy of James's copy of Numerical reasoning - ratio recipe", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": ["stats"], "ungrouped_variables": ["amount", "uv", "ratiototal", "rgcd", "units", "rawratios", "rv", "u", "lots", "ratios"], "preamble": {"js": "", "css": ""}, "statement": "<p>A&nbsp;Super Paint consists of three lequids $x$, $y$ and $z$ in the proportion&nbsp;<strong>{ratios[0]}:{ratios[1]}:{ratios[2]}</strong>.</p>", "metadata": {"description": "<p>Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.</p>\n                        <p>Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"u": {"group": "Ungrouped variables", "templateType": "anything", "definition": "//amount of each liquid\n    map(random(3..10)*ratios[j],j,0..2)", "name": "u", "description": ""}, "uv": {"group": "Ungrouped variables", "templateType": "anything", "definition": "vector(u)", "name": "uv", "description": ""}, "lots": {"group": "Ungrouped variables", "templateType": "anything", "definition": "floor(min(map(u[j]/ratios[j],j,0..2)\t))", "name": "lots", "description": ""}, "ratios": {"group": "Ungrouped variables", "templateType": "anything", "definition": "map(rawratios[j]/rgcd,j,0..2)", "name": "ratios", "description": ""}, "ratiototal": {"group": "Ungrouped variables", "templateType": "anything", "definition": "sum(ratios)", "name": "ratiototal", "description": ""}, "units": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random('litres','gallons','millilitres')", "name": "units", "description": ""}, "amount": {"group": "Ungrouped variables", "templateType": "anything", "definition": "lots*ratiototal", "name": "amount", "description": ""}, "rgcd": {"group": "Ungrouped variables", "templateType": "anything", "definition": "gcd(gcd(rawratios[0],rawratios[1]),rawratios[2])", "name": "rgcd", "description": ""}, "rawratios": {"group": "Ungrouped variables", "templateType": "anything", "definition": "shuffle([random(1..7 except 3),random(1..7 except 3),3])", "name": "rawratios", "description": ""}, "rv": {"group": "Ungrouped variables", "templateType": "anything", "definition": "vector(ratios)", "name": "rv", "description": ""}}, "name": "Kinga's copy of James's copy of Numerical reasoning - ratio recipe", "tags": [], "parts": [{"showCorrectAnswer": true, "gaps": [{"variableReplacements": [], "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "variableReplacementStrategy": "originalfirst", "minValue": "amount", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "maxValue": "amount", "scripts": {}, "mustBeReduced": false, "type": "numberentry", "allowFractions": false}], "showFeedbackIcon": true, "scripts": {}, "prompt": "<p>How many {units} of the Super Paint can be made from a stock of materials consisting of <strong>{u[0]}</strong> {units} of $x$, <strong>{u[1]}</strong>&nbsp;{units} of $y$, and <strong>{u[2]}</strong>&nbsp;{units} of $z$?</p>\n<p>[[0]] {units}</p>", "variableReplacements": [], "marks": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst"}], "functions": {"describesol": {"definition": "if(ratios[j]=1,\"$U$ is not more than $\"+u[j]+\"$.\",\"$\"+ratios[j]+\"$ is not more than $\"+u[j]+\"$, i.e. $U$ is not more than $\"+(u[j]/ratios[j])+\"$.\")", "parameters": [["j", "number"]], "language": "jme", "type": "string"}}, "advice": "<p>The proportions {ratios[0]}:{ratios[1]}:{ratios[2]} have to be preserved.</p>\n  <p>So if we use $\\simplify{{ratios[0]}*U}$ {units} of $x$ then we must use $\\simplify{{ratios[1]}*U}$ {units} of $y$ and $\\simplify{{ratios[2]}*U}$ {units} of $z$, to get $\\var{ratiototal}U$ {units} of the preparation.</p>\n  <p>We would like $U$ to be as big as possible.</p>\n  <p>As we have $\\var{u[0]}$ {units} of $x$, {describesol(0)}</p>\n  <p>As we have $\\var{u[1]}$ {units} of $y$, {describesol(1)}</p>\n  <p>As we have $\\var{u[2]}$ {units} of $z$, {describesol(2)}</p>\n  <p>So the maximum value of $U$ is&nbsp;$\\var{lots}$ and we can make $\\var{lots} \\times \\var{ratiototal} = \\var{amount}$ {units} of the preparation.</p>", "variable_groups": [], "type": "question", "contributors": [{"name": "Kinga Zaczek", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/472/"}]}]}], "contributors": [{"name": "Kinga Zaczek", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/472/"}]}