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25 July, 07:14

The difference of two numbers, a and b, is 21. The difference of 5 times a and two times b is 18. What are the values of a and b?

A.

4, 1

B.

-19, 40

C.

20, 1

D.

30, 9

E.

-8, - 29

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Answers (1)
  1. 25 July, 07:30
    0
    E. - 8, - 29

    Step-by-step explanation:

    a-b=21

    5a - 2b = 18

    Take the first equation and solve for a by adding b to each side

    a-b=21

    a-b+b=21+b

    a = 21+b

    Now substitute a=21+b into the second equation

    5a - 2b = 18

    5 (21+b) - 2b = 18

    Distribute the 5

    105 + 5b-2b = 18

    Combine like terms

    105 + 3b = 18

    Subtract 105 from each side

    105-105 + 3b = 18-105

    3b = - 87

    Divide each side by 3

    3b/3 = -87/3

    b = - 29

    if b = - 29, we can substitute it into a = 21+b

    a = 21-29

    a = - 8
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