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
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