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Math Help - two eays to solve

  1. #1
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    two eays to solve

    What are two different ways that this problem can be solved. Using a permutation I know is one but what other ways are there?


    The ratio of red marbles to green marbles in a container is 3 to 5. How many red marbles should you add to the container with n green marbles so that the probability of getting a red marble is 7/8? Give your answer in terms of n.
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  2. #2
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    Hello, chadlyter

    This is not a Permutations problem . . .


    The ratio of red marbles to green marbles in a container is 3 to 5.
    How many red marbles should you add to the container with n green marbles
    so that the probability of getting a red marble is 7/8?
    Give your answer in terms of n.
    Presently, the ratio of red to green is: . 3:5

    If there are n green marbles, the ratio is: . \frac{3}{5}n:n
    . . and there are: . \frac{3}{5}n+n\:=\:\frac{8}{5}n marbles in the container.

    We will add x red marbles.
    Then there are: . \frac{3}{5}n + x red marbles
    . . and: . \frac{8}{5}n + x marbles in the container.

    Then we have: . \frac{\dfrac{3}{5}n+x}{\dfrac{8}{5}n+x} \:=\:\frac{7}{8}\quad\Rightarrow\quad \frac{3n+5x}{8x+5x} \:=\:\frac{7}{8}

    . . 8(3n+5x) \:=\:7(8n+5x)\quad\Rightarrow\quad 24n + 40x \:=\:56n + 35x

    . . 5x \:=\:32n\quad\Rightarrow\quad\boxed{ x \:=\:\frac{32}{5}n}

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  3. #3
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    Another way?

    Could there be a different way to solve this?
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