// Numbas version: exam_results_page_options
{"name": "Lois's copy of Numerical reasoning - lottery syndicate", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"pluralise": {"definition": "return Numbas.util.pluralise(n,single,plural);", "type": "string", "language": "javascript", "parameters": [["n", "number"], ["single", "string"], ["plural", "string"]]}}, "ungrouped_variables": ["numbernames", "winnings", "name", "share", "share1", "share0", "share2", "part", "win", "total"], "name": "Lois's copy of Numerical reasoning - lottery syndicate", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Their agreement means that the winnings should go to {name[0]}, {name[1]} and {name[2]} in the ratio $\\var{share[0]}:\\var{share[1]}:\\var{share[2]}$. Think of these as being shares in the winnings.</p>\n<p>There are $\\var{share[0]}+\\var{share[1]}+\\var{share[2]} = \\var{total}$ shares in all for the &pound;{win}.</p>\n<p>Hence each share is worth $&pound;\\var{win} \\div \\var{total} = &pound;\\var{part}$.</p>\n<p>So {name[0]} gets {share[0]} {pluralise(share[0],'share','shares')} = $\\var{share[0]} \\times &pound;\\var{part} = &pound;\\var{winnings[0]}$, {name[1]} {share[1]} {pluralise(share[1],'share','shares')}&nbsp;= $\\var{share[1]} \\times &pound;\\var{part} = &pound;\\var{winnings[1]}$ and {name[2]} {share[2]}&nbsp;{pluralise(share[2],'share','shares')}&nbsp;= $\\var{share[2]} \\times &pound;\\var{part} = &pound;\\var{winnings[2]}$.</p>\n<p></p>\n<p>See this <a href=\"http://www.mathscentre.ac.uk/resources/uploaded/mc-bus-ratios-2009-1.pdf\">Mathcentre leaflet</a> for more explanation about ratios.</p>", "rulesets": {}, "parts": [{"prompt": "<p>They win &pound;{win}. How much does each get?</p>\n      <table>\n        <tr><td>{name[0]}</td><td>&pound; [[0]]</td></tr>\n        <tr><td>{name[1]}</td><td>&pound; [[1]]</td></tr>\n        <tr><td>{name[2]}</td><td>&pound; [[2]]</td></tr>\n      </table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "winnings[0]", "minValue": "winnings[0]", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "winnings[1]", "minValue": "winnings[1]", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "winnings[2]", "minValue": "winnings[2]", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>{name[0]}, {name[1]} and {name[2]} agree to buy {numbernames[total]} pounds' worth of lottery tickets, with {name[0]} contributing &pound;{share[0]}, {name[1]} contributing &pound;{share[1]} and {name[2]} contributing &pound;{share[2]}.</p>\n  <p>They agree that if they win anything with any of these tickets that it should be shared out in the same ratio as their contributions.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"numbernames": {"definition": "['zero','one','two','three','four','five','six','seven','eight','nine','ten','eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen','nineteen']", "templateType": "anything", "group": "Ungrouped variables", "name": "numbernames", "description": ""}, "winnings": {"definition": "map(x*win/total,x,share)", "templateType": "anything", "group": "Ungrouped variables", "name": "winnings", "description": ""}, "name": {"definition": "shuffle(['Bob','Terry','Cilla','Jim','Margaret','Cyril','Ethel','Horace','Beryl'])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "name", "description": ""}, "share": {"definition": "shuffle([share0,share1,share2])", "templateType": "anything", "group": "Ungrouped variables", "name": "share", "description": ""}, "share1": {"definition": "random(1..min(floor(total/2),total-1-share0)except share0)", "templateType": "anything", "group": "Ungrouped variables", "name": "share1", "description": ""}, "share0": {"definition": "random(1..floor(total/2))", "templateType": "anything", "group": "Ungrouped variables", "name": "share0", "description": ""}, "share2": {"definition": "total-share0-share1", "templateType": "anything", "group": "Ungrouped variables", "name": "share2", "description": ""}, "part": {"definition": "win/total", "templateType": "anything", "group": "Ungrouped variables", "name": "part", "description": ""}, "win": {"definition": "random(2..10)*total*5", "templateType": "anything", "group": "Ungrouped variables", "name": "win", "description": ""}, "total": {"definition": "random(6..15)", "templateType": "anything", "group": "Ungrouped variables", "name": "total", "description": ""}}, "metadata": {"description": "<p>Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.</p>\n<p>Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.</p>\n<p>(Used in Non-Calculator test.)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}