Four years ago, Danielle was 2/3 as old as Jim was. Now she is 3/4 as old as he is. How old is each now?

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  1. Jim's present age ---- x
    Danielle's present age ----- 3x/4

    4 years ago:
    Jim ---- x-4
    Danielle ----- 3x/4 - 4

    3x/4 - 4 = (2/3)(x-4)
    3x/4 - 4 = 2x/3 - 8/3
    multiply each term by 12
    9x - 48 = 8x - 32
    x = 16

    Jim is now 16, and Danielle now is 12

    4 years ago Jim was 12 and Danielle was 8
    is 2/3 of 12 equal to 8? yes!

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  2. D - 4 = 2/3 (J - 4) ...3 D - 12 = 2 J - 8

    D = 3/4 J

    substituting ... 9/4 J = 8/4 J + 4

    solve for J , then substitute back to find D

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