Question

The difference of two numbers, a and b, is 21.The difference of five times a and two times b is 18. What are the values for a and b? Answer chocies: A.)(4,1) B.)(-19,40) C.)(20,1) D.)(30,9) E.)(-8,-29). I've already tried plugging in the answers. I'm not getting the correct solution.

Answer 1

help-need this to graduate

Answer 2

Set up two equations:

a - b = 21 [The difference of two numbers, a and b, is 21]

5a - 2b = 18 [The difference of 5 times a and two times b is 18]

Use the first equation to express a in terms of b by adding b to both sides:

a = b + 21

Substitute (b + 21) for a in the second equation:

5(b + 21) - 2b = 18

Multiply out:

5b + 105 - 2b = 18

Simplify:

3b + 105 = 18

Subtract 105 from both sides:

3b = -87

Divide both sides by 3:

b = -29

Substitute -29 for b in the first equation to solve for a:

a - (-29) = 21

Simplify:

a + 29 = 21

Subtract 29 from both sides:

a = -8

(-8,-29)

Answer 3

Thanks,this really clarified the problem for me.

Answer 4

My Pleasure.

Answer 5

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