Algebra

Rosa is 14 years older than her sister amy. Three years ago, she was three times as old as amy. how old is each girl now?

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  1. ages now:
    Amy --- x
    Rosa --- x+14

    Three years ago:
    Amy --- x-3
    rosa ---- x+11

    x+11 = 3(x-3)
    x+11 = 3x - 9
    2x = 20
    x = 10

    sub into my definitions

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  2. R = Age of Rosa

    A = Age of Amy

    Rosa is 14 years older than her sister Amy.

    R = A + 14

    Three years ago, she was three times as old as amy

    Three years ago, Rosa and Amy was 3 years younger so.

    R - 3 = 3 ( A - 3 )

    Replace R with A + 14

    A + 14 - 3 = 3 ( A - 3 )

    A + 11 = 3 A - 3 * 3

    A + 11 = 3 A - 9 Add 9 to both sides

    A + 11 + 9 = 3 A - 9 + 9

    A + 20 = 3 A Subtract A to both sides

    A + 20 - A = 3 A - A

    20 = 2 A Divide both sides by 2

    20 / 2 = 2 A / 2

    10 = A

    A = 10

    R = A + 14

    R = 10 + 14

    R = 24

    Rosa is 24 year old

    Amy is 10 year old

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