Question

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?

Answer 1

18 ?= 18

Answer 2

@Kemist

Answer 3

@iGreen

Answer 4

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



To check, substitute the values -8 and -29 for a and b in the second equation:

5(-8) - 2(-29) ?= 18

Multiply out:

-40 + 58 ?= 18

Simplify:

18 = 18