// Numbas version: finer_feedback_settings
{"name": "Q6 (Calculating cars/carparts using equations) ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["num11", "num12", "num13", "num14", "num15", "num16", "cost11", "ans11", "ans12", "cost12", "ans13", "num21", "num22", "num23", "num24", "num25", "num26", "cost21", "cost22", "ans21", "ans22", "ans23", "num31", "num32", "num33", "num34", "cost31", "cost32", "ans31", "ans32"], "name": "Q6 (Calculating cars/carparts using equations) ", "tags": ["rebelmaths", "simultaneous equations", "Simultaneous equations", "teame", "word problem"], "preamble": {"css": "", "js": ""}, "advice": "<p>Have a look at this youtube video to understand simultaneous equations better:&nbsp;<a href=\"https://www.youtube.com/watch?v=Lwto-lQzmec\">Simultaneous Equations</a></p>\n<p>Part 1:</p>\n<p>To find cost of Brand A:</p>\n<p>$\\frac{((\\var{num12} \\times \\var{cost12}) - (\\var{num14} \\times \\var{cost11}))}{((\\var{num13} \\times \\var{num12}) - (\\var{num11} \\times \\var{num14}))} = &euro;\\var{ans11}$</p>\n<p>To find cost of Brand B:</p>\n<p>$\\frac{(\\var{cost12} - (\\var{num13} \\times \\var{ans11}))}{\\var{num14}} = &euro;\\var{ans12}$</p>\n<p>To find total cost of $\\var{num15}$ Brand A tyres and $\\var{num16}$ Brand B tyres:</p>\n<p>$(\\var{num15} \\times \\var{ans11}) + (\\var{num16} \\times \\var{ans12}) = &euro;\\var{ans13}$</p>\n<p>Part 2:</p>\n<p>To find cost of a new Car:</p>\n<p>$\\frac{((\\var{num22} \\times \\var{cost22}) - (\\var{num24} \\times \\var{cost21}))}{((\\var{num23} \\times \\var{num22}) - (\\var{num21} \\times \\var{num24}))} = &euro;\\var{ans21}$</p>\n<p>To find cost of a new Van:</p>\n<p>$\\frac{(\\var{cost22} - (\\var{num23} \\times \\var{ans21}))}{\\var{num24}} = &euro;\\var{ans22}$</p>\n<p>To find total cost of $\\var{num25}$ new Cars and $\\var{num26}$ new Vans:</p>\n<p>$(\\var{num25} \\times \\var{ans21}) + (\\var{num26} \\times \\var{ans22}) = &euro;\\var{ans23}$</p>\n<p>Part 3:</p>\n<p>To find cost of a Model A Car:</p>\n<p>$\\frac{((\\var{num32} \\times \\var{cost32}) - (\\var{num34} \\times \\var{cost31}))}{((\\var{num33} \\times \\var{num32}) - (\\var{num31} \\times \\var{num34}))} = &euro;\\var{ans31}$</p>\n<p>To find cost of a Model B Car:</p>\n<p>$\\frac{(\\var{cost32} - (\\var{num33} \\times \\var{ans31}))}{\\var{num34}} = &euro;\\var{ans32}$</p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\var{num31}$ cars of model A and&nbsp;$\\var{num32}$ cars of model B cost $&euro;\\var{cost31}$, while $\\var{num33}$ cars of model A &nbsp;and&nbsp;$\\var{num34}$ cars of model B cost $&euro;\\var{cost32}$. What is&nbsp;the cost of each model?</p>\n<p><em>Round to the nearest euro.</em></p>\n<p>Model A: &nbsp;&euro;[[0]]</p>\n<p>Model B: &nbsp;&euro;[[1]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Watch this video for help with the question:</p>\n<p><a href=\"https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-systems-of-equations-by-multiplication\">Video</a></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{num11}$ tyres of Brand A and&nbsp;$\\var{num12}$ tyres of Brand B cost &euro;{dpformat(cost11,2)}.&nbsp;$\\var{num13}$ tyres of Brand A and&nbsp;$\\var{num14}$ tyres of Brand B cost &euro;{dpformat(cost12,2)}. How much do&nbsp;$\\var{num15}$ tyres of Brand A and&nbsp;$\\var{num16}$ tyres of Brand B cost?</p>\n<p><em>Round to the nearest cent.</em></p>\n<p>Brand A: &nbsp;&euro;[[0]]</p>\n<p>Brand B: &nbsp;&euro;[[1]]</p>\n<p>Total: &nbsp; &nbsp; &nbsp;&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}+0.5", "strictPrecision": false, "minValue": "{ans11}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}+0.5", "strictPrecision": false, "minValue": "{ans12}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans13}+1", "strictPrecision": false, "minValue": "{ans13}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{num21}$ new Cars&nbsp;and&nbsp;$\\var{num22}$ new Vans&nbsp;cost $&euro;\\var{cost21}$, while $\\var{num23}$ new Cars and&nbsp;$\\var{num24}$ new Vans&nbsp;cost $&euro;\\var{cost22}$. Find the cost of $\\var{num25}$ new Cars and&nbsp;$\\var{num26}$ new Vans.</p>\n<p><em>Round to the nearest euro.</em></p>\n<p>New Car: &nbsp;&euro;[[0]]</p>\n<p>New Van: &nbsp;&euro;[[1]]</p>\n<p>Total: &nbsp; &nbsp; &nbsp; &nbsp;&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}", "minValue": "{ans23}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve the following:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"cost31": {"definition": "(num31*ans31)+(num32*ans32)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost31", "description": ""}, "cost32": {"definition": "(num33*ans31)+(num34*ans32)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost32", "description": ""}, "ans23": {"definition": "(num25*ans21)+(num26*ans22)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "random(11500..ans21-2000#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "random(14000..17000#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "cost12": {"definition": "(num13*ans11)+(num14*ans12)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost12", "description": ""}, "cost11": {"definition": "(num11*ans11)+(num12*ans12)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost11", "description": ""}, "num23": {"definition": "random(3..12 except [num21,num22])", "templateType": "anything", "group": "Ungrouped variables", "name": "num23", "description": ""}, "num22": {"definition": "random(3..12 except num21)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "random(3..7 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num26": {"definition": "random(3..12 except [num21,num22,num23,num24,num25])", "templateType": "anything", "group": "Ungrouped variables", "name": "num26", "description": ""}, "num25": {"definition": "random(3..12 except [num21,num22,num23,num24])", "templateType": "anything", "group": "Ungrouped variables", "name": "num25", "description": ""}, "num24": {"definition": "random(3..12 except [num21,num22,num23])", "templateType": "anything", "group": "Ungrouped variables", "name": "num24", "description": ""}, "ans12": {"definition": "random(75.5..99#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans13": {"definition": "(num15*ans11)+(num16*ans12)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13", "description": ""}, "cost21": {"definition": "(num21*ans21)+(num22*ans22)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost21", "description": ""}, "ans11": {"definition": "random(55.5..70#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "random(17000..19000#200)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "random(22000..26000#500)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "cost22": {"definition": "(num23*ans21)+(num24*ans22)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost22", "description": ""}, "num16": {"definition": "random(3..14 except [num11,num12,num13,num14,num15])", "templateType": "anything", "group": "Ungrouped variables", "name": "num16", "description": ""}, "num14": {"definition": "random(3..14 except [num11,num12,num13])", "templateType": "anything", "group": "Ungrouped variables", "name": "num14", "description": ""}, "num15": {"definition": "random(3..14 except [num11,num12,num13,num14])", "templateType": "anything", "group": "Ungrouped variables", "name": "num15", "description": ""}, "num12": {"definition": "random(3..14 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(3..14 except [num11,num12])", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num11": {"definition": "random(3..14)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num34": {"definition": "random(3..7 except [num31,num32,num33])", "templateType": "anything", "group": "Ungrouped variables", "name": "num34", "description": ""}, "num31": {"definition": "random(3..7 except [num11,num21])", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "num32": {"definition": "random(3..7 except [num31])", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}, "num33": {"definition": "random(3..7 except [num31,num32])", "templateType": "anything", "group": "Ungrouped variables", "name": "num33", "description": ""}}, "metadata": {"description": "<p>Word Problems leading to simultaneous Linear Equations</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}