Three women, Joelle, Xandra and Zoe went on a shopping spree. 30% of Joelle's spending was equal to ¹₅ of Xandra's spending. Zoe's spending was  25% less than Xandra's. If Xandra spent $156 less, she would spend the same amount of money as Zoe.

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

Joelle	Xandra	Zoe
2x4	3x4
	4x3	3x3
8 u	12 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Joelle's spending is equal to ¹₅ of Xandra's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Joelle's spending = 15 of Xandra's spending
310 of Joelle's spending =1x35x3 of Xandra's spending
310 of Joelle's spending = 315 of Xandra's spending

Joelle : Xandra
10 : 15
2 : 3

Zoe's spending in percent when compared to Xandra's
= 100% - 25%
= 75%

Xandra : Zoe
100 : 75
4 : 3

Xandra's spending is the repeated identity.  Make Xandra's spending the same.  LCM of 3 and 4 is 12.

Joelle : Xandra : Zoe
8 : 12 : 9

(b)

	Joelle	Xandra	Zoe
Before	8 u	12 u	9 u
Change		- 3 u
After	8 u	9 u	9 u

Additional amount that Xandra would have to spend less to be the same as Zoe
= 12 u - 9 u
= 3 u

3 u = 156

1 u = 156 ÷ 3 = 52

Amount that Zoe spent
= 9 u
= 9 x 52
= $468 

Answer(s): (a) 8 : 12 : 9; (b) $468