Math

The ratio of Jim's money to Peters money was 4:7 at first. After peter gave 3/14 of his money to jim, they have equal amounts of money. How much money did jim have at first?

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  1. J/P = 4/7 so J = 4 P/7

    P - 3 P/14 = J + 3 P/14

    P - 3 P/7 = J = 4 P/7

    4 P/7 = 4 P/7

    any P OR any J

    say J = 8
    then P = 14

    14 -3 (14/14) = ?? 8 + 3(14/14)
    well
    11 = 11 sure enough :)

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  2. Let peter have Jim have $4x. Then the given ratio means that Peter has $7x.

    Since Jim spent half his money, he now has $2x dollars.

    Peter spent $60 and thus now has $(7x-60).

    The final ratio of Jim's money to Peter's money is therefore 2x : (7x-60). This is given as 1:2.

    Now we just need to solve the proportion by cross-multiplying.

    2x : (7x - 60) = 1 : 2

    1*(7x - 60) = 2*2x

    7x - 60 = 4x

    3x = 60

    x = 20. Therefore Jim originally had $4x = $80.

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