// Numbas version: exam_results_page_options {"name": "Numerical reasoning - lottery syndicate", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Numerical reasoning - lottery syndicate", "tags": ["lottery", "maths-aid", "money", "numerical reasoning", "ratio", "shares"], "metadata": {"description": "

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.

\n

Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.

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{names[0]}, {names[1]} and {names[2]} agree to buy {numbernames[total]} pounds' worth of lottery tickets, with {names[0]} contributing £{share[0]}, {names[1]} contributing £{share[1]} and {names[2]} contributing £{share[2]}.

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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.

", "advice": "

Their agreement means that the winnings should go to {names[0]}, {names[1]} and {names[2]} in the ratio $\\var{share[0]}:\\var{share[1]}:\\var{share[2]}$. Think of these as being shares in the winnings.

\n

There are $\\var{share[0]}+\\var{share[1]}+\\var{share[2]} = \\var{total}$ shares in all for the £{win}.

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Hence each share is worth $£\\var{win} \\div \\var{total} = £\\var{part}$.

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So {names[0]} gets {share[0]} {pluralise(share[0],'share','shares')} = $\\var{share[0]} \\times £\\var{part} = £\\var{winnings[0]}$, {names[1]} {share[1]} {pluralise(share[1],'share','shares')} = $\\var{share[1]} \\times £\\var{part} = £\\var{winnings[1]}$ and {names[2]} {share[2]} {pluralise(share[2],'share','shares')} = $\\var{share[2]} \\times £\\var{part} = £\\var{winnings[2]}$.

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They win £{win}. How much does each get?

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
{names[0]}£ [[0]]
{names[1]}£ [[1]]
{names[2]}£ [[2]]
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