Two numbers differ by 5. Seven times the smaller plus four times the larger is 108. Find the number

Question

Two numbers differ by 5. Seven times the smaller plus four times the larger is 108. Find the number

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Thanh Thu 6 months 2021-08-13T22:29:22+00:00 1 Answers 3 views 0

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    2021-08-13T22:31:12+00:00

    Answer:

    8 and 13

    Step-by-step explanation:

    Let the two numbers be x and y

    If the two numbers differs by 5, then;

    y-x = 5 …1

    x is the smaller

    y is the larger

    If seven times the smaller plus four times the larger is 108, this is expressed as;

    7x + 4y = 108 … 2

    From 1;

    y = 5 + x …. 3

    Substitute 3 into 2;

    From 2;

    7x + 4y = 108

    7x + 4(5+x) = 108

    7x + 20 + 4x = 108

    11x + 20 = 108

    11x = 108-20

    11x = 88

    x = 88/11

    x = 8

    Since y = 5+x

    y = 5 + 8

    y = 13

    hence the numbers are 8 and 13

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