Three women, Cindy, Joelle and Mary went on a shopping spree. 30% of Cindy's spending was equal to ¹₂ of Joelle's spending. Mary's spending was  40% less than Joelle's. If Joelle spent $456 less, she would spend the same amount of money as Mary.

1. Find the ratio of Cindy's spending to Joelle's to Mary's.
2. How much did Mary spend?

Cindy	Joelle	Mary
5x5	3x5
	5x3	3x3
25 u	15 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Cindy's spending is equal to ¹₂ of Joelle's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Cindy's spending = 12 of Joelle's spending
310 of Cindy's spending =1x32x3 of Joelle's spending
310 of Cindy's spending = 36 of Joelle's spending

Cindy : Joelle
10 : 6
5 : 3

Mary's spending in percent when compared to Joelle's
= 100% - 40%
= 60%

Joelle : Mary
100 : 60
5 : 3

Joelle's spending is the repeated identity.  Make Joelle's spending the same.  LCM of 3 and 5 is 15.

Cindy : Joelle : Mary
25 : 15 : 9

(b)

	Cindy	Joelle	Mary
Before	25 u	15 u	9 u
Change		- 6 u
After	25 u	9 u	9 u

Additional amount that Joelle would have to spend less to be the same as Mary
= 15 u - 9 u
= 6 u

6 u = 456

1 u = 456 ÷ 6 = 76

Amount that Mary spent
= 9 u
= 9 x 76
= $684 

Answer(s): (a) 25 : 15 : 9; (b) $684