Math

The difference of two number is seven. when the larger number is decreased by five, then doubled, it is five more than the small number. Find the numbers.

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  1. let the larger number be x
    then the smaller is x-7

    "the larger number is decreased by five, then doubled" ---> 2(x-5)

    2(x-5) = x-7 +5
    2x - 10 = x - 2
    x = 8

    Finish it up, and check

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  2. a = larger number

    b = smaller number

    The difference of two number is seven mean:

    a - b = 7

    a - b = 7 Add b to both sides

    a - b + b = 7 + b

    a = 7 + b

    a = b + 7

    When the larger number is decreased by five, then doubled, it is five more than the small number mean:

    ( a - 5 ) * 2 = b + 5

    Replace a = b + 7 in this equation

    ( b + 7 - 5 ) * 2 = b + 5

    ( b + 2 ) * 2 = b + 5

    2 * b + 2 * 2 = b + 5

    2 b + 4 = b + 5 Subtract b to both sides

    2 b + 4 - b = b + 5 - b

    b + 4 = 5 Subtract 4 to both sides

    b + 4 - 4 = 5 - 4

    b = 1

    a = b + 7 = 1 + 7 = 8

    a = 8

    Proof:

    a - b = 7

    8 - 1 = 7

    ( a - 5 ) * 2 = b + 5

    ( 8 - 5 ) * 2 = 1 + 5

    3 * 2 = 6

    6 = 6

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