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Math Help - ratio of apples

  1. #1
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    ratio of apples

    Dear Sir
    I would be grateful if you can help me to solve the the below questions
    thanks
    Kingsman


    At the party, each child had either 1 apple or 2 apples. If the ratio of the number of children to the number of apples was 5: 8, what fraction of the children had 2 apples each?
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  2. #2
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    Quote Originally Posted by kingman View Post
    Dear Sir
    I would be grateful if you can help me to solve the the below questions
    thanks
    Kingsman


    At the party, each child had either 1 apple or 2 apples. If the ratio of the number of children to the number of apples was 5: 8, what fraction of the children had 2 apples each?
    2 + 2 + 2 + 1 + 1 = 8
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  3. #3
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    Dear Sir,
    Can you show me how to do this question algebraically.
    Thanks
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  4. #4
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    Hello, kingman!

    At the party, each child had either 1 apple or 2 apples.
    If the ratio of the number of children to the number of apples was 5: 8,
    what fraction of the children had 2 apples each?

    Let \,A = number of children with 1 apple.
    Let \,B = number of children with 2 apples.

    Then there were: . A+B children.

    And there were: . A + 2B apples.

    . . We want the fraction: . \dfrac{B}{A+B}


    We are told that: . \dfrac{\text{children}}{\text{apples}} \:=\:\dfrac{5}{8}

    . . . .So we have: . \dfrac{A+B}{A+2B} \:=\:\dfrac{5}{8} <br />

    which simplifies to: . . . \dfrac{A}{B} \;=\;\dfrac{2}{3}


    Add 1 to both sides: . \dfrac{A}{B} + 1 \;=\;\dfrac{2}{3} + 1 \quad\Rightarrow\quad \dfrac{A+B}{B} \;=\;\dfrac{5}{3}


    . . Therefore: . \dfrac{B}{A+B} \;=\;\dfrac{3}{5}
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  5. #5
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    Dear Soroban.
    You are a fantastic problem solver and I love your approach to the problem very much.Crystal Clear!
    Thousand Thanks
    Kingman
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  6. #6
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    Dear Sir,
    Can this problem be solved by looking at the remainder when the number of apples ( 8x ) is divided by the number of children ( 5x)
    Thanks
    Kingman
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