// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Q4 Lotto Ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Split winnings in a ratio</p>\n<p>rebel</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"condition": "  ", "maxRuns": 100}, "statement": "<p>Solve the following prize funds questions, to the nearest Euro:</p>", "ungrouped_variables": ["number1", "number2", "number3", "number4", "prize1", "prize2", "prize3", "number5", "number6", "number7", "number8", "number9", "number10", "ans1", "ans2", "ans3", "ans4", "ans5", "ans6", "ans7", "ans8", "ans9"], "variable_groups": [], "variables": {"ans7": {"description": "", "definition": "({prize3}/{number9})*{number8}", "group": "Ungrouped variables", "name": "ans7", "templateType": "anything"}, "prize3": {"description": "", "definition": "random(650..950)*number9", "group": "Ungrouped variables", "name": "prize3", "templateType": "anything"}, "ans5": {"description": "", "definition": "({prize2}/{number7}) * {number5}", "group": "Ungrouped variables", "name": "ans5", "templateType": "anything"}, "number3": {"description": "", "definition": "random(8..10)-(number1+number2)", "group": "Ungrouped variables", "name": "number3", "templateType": "anything"}, "number8": {"description": "", "definition": "random(1.5..4#0.5)", "group": "Ungrouped variables", "name": "number8", "templateType": "anything"}, "ans1": {"description": "", "definition": "{prize1}/({number1}+{number2}+{number3}) * {number1} *1000000 ", "group": "Ungrouped variables", "name": "ans1", "templateType": "anything"}, "ans9": {"description": "", "definition": "{ans7}+{ans8}+{prize3}", "group": "Ungrouped variables", "name": "ans9", "templateType": "anything"}, "number2": {"description": "", "definition": "random(1.5..4.5 except {number1})", "group": "Ungrouped variables", "name": "number2", "templateType": "anything"}, "number6": {"description": "", "definition": "random(1.5..4#0.5 except {number4} except {number5})", "group": "Ungrouped variables", "name": "number6", "templateType": "anything"}, "ans2": {"description": "", "definition": "{prize1}/({number1}+{number2}+{number3}) * {number2} *1000000   ", "group": "Ungrouped variables", "name": "ans2", "templateType": "anything"}, "ans6": {"description": "", "definition": "({prize2}/{number7}) * {number6}", "group": "Ungrouped variables", "name": "ans6", "templateType": "anything"}, "ans3": {"description": "", "definition": "{prize1}/({number1}+{number2}+{number3}) * {number3} *1000000  ", "group": "Ungrouped variables", "name": "ans3", "templateType": "anything"}, "ans8": {"description": "", "definition": "({prize3}/{number9})*{number10}", "group": "Ungrouped variables", "name": "ans8", "templateType": "anything"}, "number1": {"description": "", "definition": "random(1.5..2.5)", "group": "Ungrouped variables", "name": "number1", "templateType": "anything"}, "ans4": {"description": "", "definition": "({prize2}/{number7}) * {number4}", "group": "Ungrouped variables", "name": "ans4", "templateType": "anything"}, "prize1": {"description": "", "definition": "(number1+number2+number3)* random(3.25..5.75#0.5)*0.1", "group": "Ungrouped variables", "name": "prize1", "templateType": "anything"}, "number9": {"description": "", "definition": "random(1.5..4#0.5 except {number8})", "group": "Ungrouped variables", "name": "number9", "templateType": "anything"}, "number10": {"description": "", "definition": "random(1.5..4#0.5 except {number8} except {number9})", "group": "Ungrouped variables", "name": "number10", "templateType": "anything"}, "number7": {"description": "", "definition": "random(7..9#0.5)", "group": "Ungrouped variables", "name": "number7", "templateType": "anything"}, "number5": {"description": "", "definition": "random(1.5..4#0.5 except {number4})", "group": "Ungrouped variables", "name": "number5", "templateType": "anything"}, "prize2": {"description": "", "definition": "random(29000..50000#500)*number7", "group": "Ungrouped variables", "name": "prize2", "templateType": "anything"}, "number4": {"description": "", "definition": "random(1.5..4#0.5)", "group": "Ungrouped variables", "name": "number4", "templateType": "anything"}}, "parts": [{"marks": 0, "stepsPenalty": 0, "steps": [{"marks": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "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 winnings 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": [], "extendBaseMarkingAlgorithm": true, "type": "information", "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true}], "gaps": [{"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precisionType": "dp", "precision": 0, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "strictPrecision": false, "showPrecisionHint": false, "maxValue": "{ans1}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}, {"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precisionType": "dp", "precision": 0, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "strictPrecision": false, "showPrecisionHint": false, "maxValue": "{ans2}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}, {"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precisionType": "dp", "precision": 0, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "strictPrecision": false, "showPrecisionHint": false, "maxValue": "{ans3}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}], "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": [], "type": "gapfill", "scripts": {}, "unitTests": [], "showCorrectAnswer": true, "sortAnswers": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}, {"marks": 0, "stepsPenalty": 0, "steps": [{"marks": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "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": [], "extendBaseMarkingAlgorithm": true, "type": "information", "scripts": {}, "customMarkingAlgorithm": "", "showCorrectAnswer": true}], "gaps": [{"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precisionType": "dp", "precision": 0, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "strictPrecision": false, "showPrecisionHint": false, "maxValue": "{ans4}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}, {"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precisionType": "dp", "precision": 0, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{ans5}", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "strictPrecision": false, "showPrecisionHint": false, "maxValue": "{ans5}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}, {"precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "scripts": {}, "correctAnswerStyle": "plain", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precisionType": "dp", "precision": 0, "marks": 1, "precisionPartialCredit": 0, "correctAnswerFraction": false, "mustBeReducedPC": 0, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{ans6}", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "strictPrecision": false, "showPrecisionHint": false, "maxValue": "{ans6}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}], "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": [], "type": "gapfill", "scripts": {}, "unitTests": [], "showCorrectAnswer": true, "sortAnswers": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}, {"marks": 0, "gaps": [{"marks": 1, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "scripts": {}, "minValue": "{ans7}", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "mustBeReduced": false, "maxValue": "{ans7}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"marks": 1, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "scripts": {}, "minValue": "{ans8}", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "mustBeReduced": false, "maxValue": "{ans8}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"marks": 1, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "mustBeReducedPC": 0, "variableReplacements": [], "type": "numberentry", "scripts": {}, "minValue": "{ans9}", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "mustBeReduced": false, "maxValue": "{ans9}", "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}], "prompt": "<p>A prize fund is divided between A, B and C in the ratio $\\var{number8}:\\var{number9}:\\var{number10}$</p>\n<p>B's share is &euro;$\\var{prize3}$</p>\n<p>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": [], "type": "gapfill", "scripts": {}, "unitTests": [], "showCorrectAnswer": true, "sortAnswers": false, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": ""}], "tags": [], "rulesets": {}, "name": "Simon's copy of Q4 Lotto Ratio", "functions": {}, "advice": "<p><strong>(a)</strong></p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times \\var{number1} \\times 1000000 = \\var{dpformat(ans1,2)}$</p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times&nbsp;\\var{number2} \\times 1000000 = \\var{dpformat(ans2,2)}$</p>\n<p>$\\frac{\\var{prize1}}{(\\var{number1} + \\var{number2} + \\var{number3}) } \\times&nbsp;\\var{number3} \\times 1000000 = \\var{dpformat(ans3,2)}$</p>\n<p><em></em></p>\n<p><strong>(b)</strong></p>\n<p>1 part is worth $\\frac{\\var{prize2}}{\\var{number7}}=\\var{prize2/number7}$</p>\n<p>Therefore each person gets:</p>\n<p>$\\var{prize2/number7} \\times&nbsp;\\var{number4} = \\var{dpformat(ans4,2)}$</p>\n<p>$\\var{prize2/number7} \\times&nbsp;\\var{number5} = \\var{dpformat(ans5,2)}$</p>\n<p>$\\var{prize2/number7} \\times&nbsp;\\var{number6} = \\var{dpformat(ans6,2)}$</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>$\\frac{\\var{prize3}}{\\var{number9}} \\times&nbsp;\\var{number8} = \\var{dpformat(ans7,2)}$</p>\n<p>$\\frac{\\var{prize3}}{\\var{number9}} \\times&nbsp;\\var{number10} = \\var{dpformat(ans8,2)}$</p>\n<p>$\\var{ans7}&nbsp;+ \\var{ans8} + \\var{prize3}&nbsp;= \\var{dpformat(ans9,2)}$</p>", "preamble": {"css": "", "js": ""}, "extensions": [], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}