// Numbas version: finer_feedback_settings
{"name": "Q4 Lotto Ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["number1", "number2", "number3", "number4", "prize1", "prize2", "prize3", "number5", "number6", "number7", "number8", "number9", "number10", "ans1", "ans2", "ans3", "ans4", "ans5", "ans6", "ans7", "ans8", "ans9"], "name": "Q4 Lotto Ratio", "tags": ["ratio", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "<p><em>Part 1:</em></p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times \\var{number1} \\times 1000000 = \\var{ans1}$</p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times&nbsp;\\var{number2} \\times 1000000 = \\var{ans2}$</p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times&nbsp;\\var{number3} \\times 1000000 = \\var{ans3}$</p>\n<p><em></em></p>\n<p><em>Part 2:</em></p>\n<p>$\\frac{\\var{prize2}}{\\var{number7}} \\times&nbsp;\\var{number4} = \\var{ans4}$</p>\n<p>$\\frac{\\var{prize2}}{\\var{number7}} \\times&nbsp;\\var{number5} = \\var{ans5}$</p>\n<p>$\\frac{\\var{prize2}}{\\var{number7}} \\times&nbsp;\\var{number6} = \\var{ans6}$</p>\n<p></p>\n<p><em>Part 3:</em></p>\n<p>$\\frac{\\var{prize3}}{\\var{number9}} \\times&nbsp;\\var{number8} = \\var{ans7}$</p>\n<p>$\\frac{\\var{prize3}}{\\var{number9}} \\times&nbsp;\\var{number10} = \\var{ans8}$</p>\n<p>$\\var{ans7}&nbsp;+ \\var{ans8} + \\var{prize3}&nbsp;= \\var{ans9}$</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Three people in a syndicate share a Lotto prize in the ratio $\\var{number1}:\\var{number2}:\\var{number3}$. If the total prize won is &euro;$\\var{prize1}$ million, how much does each person in the syndicate get?</p>\n<p><em>(Do not answer in millions)</em></p>\n<p>&euro;[[0]]</p>\n<p>&euro;[[1]]</p>\n<p>&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Hint: 1 million is 1,000,000</p>\n<p>Convert $\\var{prize1}$ million to a nice number form by multiplying by 1,000,000.</p>\n<p>We need to divide the wimmings up into smaller pieces and then share those pieces out according to the ratio. To find how many little pieces we need to make we add</p>\n<p>$\\var{number1}$ +&nbsp;$\\var{number2}$ +&nbsp;$\\var{number3}$.</p>\n<p>Divide the prize into this many pieces.</p>\n<p>Multiply by each number from the ratio to see how much each person wins.</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": "{ans1}", "strictPrecision": false, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "strictPrecision": false, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "strictPrecision": false, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Four people in a syndicate share a Lotto prize in the ratio $\\var{number4}:\\var{number5}:\\var{number6}:\\var{number7}$.</p>\n<p>In the recent draw, the person with the largest share won &euro;$\\var{prize2}$. How much did each of the others win?</p>\n<p>&euro;[[0]]</p>\n<p>&euro;[[1]]</p>\n<p>&euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>The person with the largest share got&nbsp;$\\var{number7}$ of the total&nbsp;$\\var{number4}$ +&nbsp;$\\var{number5}$ +&nbsp;$\\var{number6}$ +&nbsp;$\\var{number7}$ parts. Divide&nbsp;$\\var{prize2}$ by&nbsp;$\\var{number7}$ to see how much each part was. The first person got&nbsp;$\\var{number4}$ of these parts.</p>\n<p>How much did they get?</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": "{ans4}", "strictPrecision": false, "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans5}", "strictPrecision": false, "minValue": "{ans5}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans6}", "strictPrecision": false, "minValue": "{ans6}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>A prize fund is divided between A, B and C in the ratio $\\var{number8}:\\var{number9}:\\var{number10}$. If B's share is &euro;$\\var{prize3}$; find how much A gets, how much C gets and the total prize fund.</p>\n<p>A gets: &euro;[[0]]</p>\n<p>C gets: &euro;[[1]]</p>\n<p>Total prize fund: &euro;[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans7}", "minValue": "{ans7}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans8}", "minValue": "{ans8}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans9}", "minValue": "{ans9}", "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 prize funds questions, to the nearest Euro:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "  "}, "variables": {"ans8": {"definition": "({prize3}/{number9})*{number10}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans8", "description": ""}, "ans9": {"definition": "{ans7}+{ans8}+{prize3}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans9", "description": ""}, "ans1": {"definition": "{prize1}/({number1}+{number2}+{number3}) * {number1} *1000000 ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "{prize1}/({number1}+{number2}+{number3}) * {number2} *1000000   ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "{prize1}/({number1}+{number2}+{number3}) * {number3} *1000000  ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "({prize2}/{number7}) * {number4}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans5": {"definition": "({prize2}/{number7}) * {number5}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "ans6": {"definition": "({prize2}/{number7}) * {number6}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "ans7": {"definition": "({prize3}/{number9})*{number8}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans7", "description": ""}, "prize2": {"definition": "random(29000..50000#500)*number7", "templateType": "anything", "group": "Ungrouped variables", "name": "prize2", "description": ""}, "prize3": {"definition": "random(650..950)*number9", "templateType": "anything", "group": "Ungrouped variables", "name": "prize3", "description": ""}, "prize1": {"definition": "(number1+number2+number3)* random(3.25..5.75#0.5)*0.1", "templateType": "anything", "group": "Ungrouped variables", "name": "prize1", "description": ""}, "number10": {"definition": "random(1.5..4#0.5 except {number8} except {number9})", "templateType": "anything", "group": "Ungrouped variables", "name": "number10", "description": ""}, "number6": {"definition": "random(1.5..4#0.5 except {number4} except {number5})", "templateType": "anything", "group": "Ungrouped variables", "name": "number6", "description": ""}, "number7": {"definition": "random(7..9#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number7", "description": ""}, "number4": {"definition": "random(1.5..4#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number4", "description": ""}, "number5": {"definition": "random(1.5..4#0.5 except {number4})", "templateType": "anything", "group": "Ungrouped variables", "name": "number5", "description": ""}, "number2": {"definition": "random(1.5..4.5 except {number1})", "templateType": "anything", "group": "Ungrouped variables", "name": "number2", "description": ""}, "number3": {"definition": "random(8..10)-(number1+number2)", "templateType": "anything", "group": "Ungrouped variables", "name": "number3", "description": ""}, "number1": {"definition": "random(1.5..2.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number1", "description": ""}, "number8": {"definition": "random(1.5..4#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "number8", "description": ""}, "number9": {"definition": "random(1.5..4#0.5 except {number8})", "templateType": "anything", "group": "Ungrouped variables", "name": "number9", "description": ""}}, "metadata": {"description": "<p>Split winnings in a ratio</p>\n<p>rebel</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/"}]}