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11 September, 17:17

The larger of two numbers is 15 more than the smaller number. Five times the larger number is 40 more than twelve times the smaller number. Find the numbers.

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  1. 11 September, 20:24
    0
    10, 20

    Step-by-step explanation:

    x = larger number

    y = smaller number

    ...

    x = 10+y

    5x=40+6y

    ...

    Substitution of x into the second equation

    5 (10+y) = 40+6y

    50 + 5y = 40 + 6y

    ...

    Isolate y

    5y - 6y = 40 - 50

    -y = - 10

    Divide both sides by - 1

    y=10 is the smaller number

    ...

    Rearrange x = 10+y to y = x-10

    Substitute into 5x=40+6y

    5x = 40 + 6 (x-10)

    5x = 40 + 6x - 60

    ...

    Isolate x

    5x - 6x = 40 - 60

    -x = - 20

    Divide both sides by - 1

    X=20 is the larger number
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