The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?

Question

The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?

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MichaelMet 3 years 2021-08-21T15:06:11+00:00 1 Answers 1 views 0

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    2021-08-21T15:07:52+00:00

    Answer:

    The first number is 16

    The second number is 6

    The third number is 64

    Step-by-step explanation:

    The information from the word problem are;

    The count of the numbers in the sum = 3 numbers

    The value of the sum of the three numbers = 86

    The value of the third number = 4 × The value of the first number

    The value of the first number = 10 + The value of the second

    Let ‘x’ represent the first number, let ‘y’ represent the second number and let ‘z’ represent the third number, we have;

    x + y + z = 86…(1)

    z = 4 × x…(2)

    x = y + 10…(3)

    From equation (3), we get;

    x = y + 10

    ∴ y = x – 10…(4)

    Substituting the value of z from equation (2) and the value of y from equation (4) in equation (1) gives;

    x + y + z = 86

    z = 4 × x = 4·x

    y = x – 10

    ∴ x + y + z = x + (x – 10) + 4·x = 86

    x + (x – 10) + 4·x = x + x – 10 + 4·x = 6·x – 10 = 86

    6·x = 86 + 10 = 96

    ∴ x = 96/6 = 16

    x = 16

    From equation (2), we get;

    z = 4 × x

    ∴ z = 4 × 16 = 64

    z = 64

    From equation (4), we get

    y = x – 10

    ∴ y = 16 – 10 = 6

    y = 6

    Therefore; x = 16, y = 6, and z = 64

    The numbers are 16, 6, and 64

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