// Numbas version: finer_feedback_settings
{"name": "Q5 (Calculating wages using algebraic 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", "wages1", "num13", "ans11", "ans12", "ans21", "ans22", "num21", "num22", "num23", "wages2", "num31", "num32", "wages3", "num33", "ans31", "ans32", "num41", "num42", "wages41", "num43", "wages42", "ans41", "ans42"], "name": "Q5 (Calculating wages using algebraic equations)", "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "teame"], "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>Tradesman:</p>\n<p>Find the Labourer's wage first, then:</p>\n<p>$\\var{ans12} + \\var{num13} = &euro;\\var{ans11}$</p>\n<p>Labourer:</p>\n<p>$\\frac{\\var{wages1} - (\\var{num11} \\times \\var{num13})}{(\\var{num11} + \\var{num12})} = &euro;\\var{ans12}$</p>\n<p>Part 2:</p>\n<p>First identify the 2 simultaneous equations;</p>\n<p>L + T = $\\var{num21}$</p>\n<p>$\\var{num22}$L + $\\var{num23}T$ = $\\var{wages2}$</p>\n<p>No. of Labourers:</p>\n<p>Find the no. of Tradesmen first, then:</p>\n<p>$\\var{num21} - \\var{ans22} =&nbsp;\\var{ans21}$</p>\n<p>No. of Tradesmen:</p>\n<p>$\\frac{((\\var{wages2} \\times 1) - (\\var{num22} \\times \\var{num21}))}{((\\var{num23} \\times 1) - (\\var{num22} \\times 1))} = \\var{ans22}$</p>\n<p>Part 3:</p>\n<p>Tradesman:</p>\n<p>Find the Labourer's wage first, then:</p>\n<p>$\\var{ans32} + \\var{num33} = &euro;\\var{ans31}$</p>\n<p>Labourer:</p>\n<p>$\\frac{\\var{wages3} - (\\var{num31} \\times \\var{num33})}{(\\var{num31} + \\var{num32})} = &euro;\\var{ans32}$</p>\n<p>Part 4:</p>\n<p>Tradesman:</p>\n<p>Find the Labourer's wage first, then:</p>\n<p>$\\var{wages42} - (\\var{num43} \\times \\var{num41}) = &euro;\\var{ans41}$</p>\n<p>Labourer:</p>\n<p>$\\frac{\\var{wages41} - (\\var{num41} \\times \\var{wages42})}{(\\var{num42} - (\\var{num41} \\times \\var{num43}))} = &euro;\\var{ans42}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\var{num41}$ tradesmen and&nbsp;$\\var{num42}$ labourers earn&nbsp;$&euro;\\var{wages41}$ per week while 1 tradesman and&nbsp;$\\var{num43}$ labourers earn $&euro;\\var{wages42}$ per week. Find&nbsp;the earnings for 1 tradesman and 1 labourer.</p>\n<p>Tradesmen: &nbsp;&euro;[[0]]</p>\n<p>Labourer: &nbsp; &nbsp; &euro;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Create two simultaneous equations to describe the information given in the question.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans42}+0.5", "strictPrecision": false, "minValue": "{ans42}-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": "{ans41}+0.5", "strictPrecision": false, "minValue": "{ans41}-0.5", "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>$\\var{num11}$ tradesmen and&nbsp;$\\var{num12}$ labourers earn&nbsp;$&euro;\\var{wages1}$ between them to do a job. If a tradesman earns&nbsp;$&euro;\\var{num13}$ more than a labourer, calculate the earnings for a tradesman and a labourer.</p>\n<p>Tradesmen: &nbsp;&euro;[[0]]</p>\n<p>Labourer: &nbsp; &nbsp; &euro;[[1]]</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}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{num21}$ workmen on a building site earn a total of&nbsp;$&euro;\\var{wages2}$ between them per week. Labourers are paid&nbsp;$&euro;\\var{num22}$ per week and Tradesmen are paid&nbsp;$&euro;\\var{num23}$ per week. How many of each is employed?</p>\n<p>[[0]] &nbsp;Labourers</p>\n<p>[[1]] Tradesmen</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\var{num31}$ tradesmen and&nbsp;$\\var{num32}$ labourers earn&nbsp;$&euro;\\var{wages3}$ between them to do a job. If a tradesman earns&nbsp;$&euro;\\var{num33}$ more than a labour, calculate the earnings for a tradesman and a labourer.</p>\n<p>Tradesmen: &nbsp;&euro;[[0]]</p>\n<p>Labourer: &nbsp; &nbsp; &euro;[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-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": "{ans32}+0.5", "strictPrecision": false, "minValue": "{ans32}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Calculate the following, to the nearest cent!!</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"wages41": {"definition": "random(9000..11000)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages41", "description": ""}, "wages42": {"definition": "random(2405..2795#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages42", "description": ""}, "ans22": {"definition": "random(3..12 except ans21)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "wages3": {"definition": "random(7005..8995#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages3", "description": ""}, "wages2": {"definition": "(ans21*num22)+(ans22*num23)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages2", "description": ""}, "wages1": {"definition": "random(8000..9000)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages1", "description": ""}, "ans41": {"definition": "(wages41-(wages42*num41))/(num42 -(num41*num43))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans42": {"definition": "wages42-(num43*ans41)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num23": {"definition": "random(num22+140..800#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num23", "description": ""}, "num22": {"definition": "random(500..600#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "ans21+ans22", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num41": {"definition": "random(5..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "num41", "description": ""}, "num43": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "num43", "description": ""}, "num42": {"definition": "random(7..9 except num41)", "templateType": "anything", "group": "Ungrouped variables", "name": "num42", "description": ""}, "ans12": {"definition": "(wages1-(num11*num13))/(num11+num12)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "ans12+num13", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "ans32+num33", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(wages3-(num31*num33))/(num31+num32)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "num12": {"definition": "random(4..7 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(71..89 except[80])", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num11": {"definition": "random(7..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num31": {"definition": "random(4..11 except [num11,num21])", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "num32": {"definition": "random(4..11 except [num11,num21,num31])", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}, "num33": {"definition": "random(66..84 except[70,75,80])", "templateType": "anything", "group": "Ungrouped variables", "name": "num33", "description": ""}}, "metadata": {"description": "<p>Calculating wages using algebraic 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/"}]}