// Numbas version: exam_results_page_options
{"name": "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": [{"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 $\"+(u[j]/ratios[j])+\"$.\")", "type": "string", "language": "jme", "parameters": [["j", "number"]]}}, "name": "Numerical reasoning - ratio recipe", "tags": ["chain rule", "proportion", "ratio"], "type": "question", "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>", "rulesets": {}, "parts": [{"prompt": "<p>How many {units} of the preparation 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>", "marks": 0, "gaps": [{"marks": 1, "maxValue": "amount", "minValue": "amount", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "extensions": ["stats"], "statement": "<p>A certain preparation consists of liquids $x$, $y$ and $z$ in the proportion&nbsp;<strong>{ratios[0]}:{ratios[1]}:{ratios[2]}</strong>.</p>", "variable_groups": [], "progress": "ready", "preamble": {"css": "", "js": ""}, "variables": {"rv": {"definition": "vector(ratios)", "templateType": "anything", "group": "Ungrouped variables", "name": "rv", "description": ""}, "rawratios": {"definition": "shuffle([random(1..7 except 3),random(1..7 except 3),3])", "templateType": "anything", "group": "Ungrouped variables", "name": "rawratios", "description": ""}, "lots": {"definition": "floor(min(map(u[j]/ratios[j],j,0..2)\t))", "templateType": "anything", "group": "Ungrouped variables", "name": "lots", "description": ""}, "uv": {"definition": "vector(u)", "templateType": "anything", "group": "Ungrouped variables", "name": "uv", "description": ""}, "rgcd": {"definition": "gcd(gcd(rawratios[0],rawratios[1]),rawratios[2])", "templateType": "anything", "group": "Ungrouped variables", "name": "rgcd", "description": ""}, "amount": {"definition": "lots*ratiototal", "templateType": "anything", "group": "Ungrouped variables", "name": "amount", "description": ""}, "u": {"definition": "//amount of each liquid\n    map(random(3..10)*ratios[j],j,0..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "ratios": {"definition": "map(rawratios[j]/rgcd,j,0..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ratios", "description": ""}, "units": {"definition": "random('litres','gallons','millilitres')", "templateType": "anything", "group": "Ungrouped variables", "name": "units", "description": ""}, "ratiototal": {"definition": "sum(ratios)", "templateType": "anything", "group": "Ungrouped variables", "name": "ratiototal", "description": ""}}, "metadata": {"notes": "", "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"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}