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Math Help - Ratio problem

  1. #1
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    Smile Ratio problem

    Hope someone can help with this problem:

    On a sports day of a school, each competitor was given 3 drink coupons while each non-competitor was given 2 drink coupons. The ratio of the numnber of pupils to the number of coupons given was 6:17. What fraction of the pupils in the school competed in the sports day?

    Appreciate if you can show detail workings.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Lets say there were x xompetitors and y non competitors
    So total noumber of people = x+y

    No . coupons for competitors = 3x

    No. of coupons for non-competitors = 2y

    So total number of coupons = 2y+3x

    Hence

    \frac{x+y}{2y+3x} = \frac{6}{17}

    Now go ahead

    Spoiler:
    17x+17y = 12y+18x

    5y = x

    But we need to get the fraction of students who participated with total number of students

    \frac{x}{x+y} = \frac{5y}{y+5y}= \frac{5}{6}
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