Question

Wendy's allowance is 9/5 of Candice's allowance. If Wendy gives $20 of her allowance
to Candice, they will both have the same amount of allowance. What is Wendy’s
allowance?
(1) $140
(2) $90
(3) $50
(4) $36

Answer 1

c = Candice's allowance

w = Wendy's allowance

Wendy's allowance is 9 / 5 of Candice's allowance means:

w / c = 9 / 5

Multiply both sides by c

w = 9 / 5 c

When Wendy gives $20 of allowance to Candice then:

Wendy will have $20 less than she has.

Candice will have $20 more than she has.

If Wendy gives $20 of her allowance to Candice, they will both have the same amount of allowance means:

w - 20 = c + 20

Replace w with 9 / 5 c in this equation

9 / 5 c - 20 = c + 20

Add 20 to both nsides

9 / 5 c = c + 40

Subtract c to both sides

9 / 5 c - c = 40

9 / 5 c - 5 / 5 c = 40

4 / 5 c = 40

Multiply both sides by 5

4 c = 200

Divide both sides by 4

c = 50

w = 9 / 5 c = 9 ∙ 50 / 5 = 450 / 5 = 90

Wendy's allowance = $90

Candice's allowance = $ 50

Answer:

(2) $90

Check result:

w / c = 90 / 50 = 10 ∙ 9 / 10 ∙ 5 = 9 / 5

w - 20 = c + 20

90 - 20 = 50 + 20

70 = 70