Three women, Winnie, Yen and Xandra went on a shopping spree. 30% of Winnie's spending was equal to ¹₅ of Yen's spending. Xandra's spending was  25% less than Yen's. If Yen spent $315 less, she would spend the same amount of money as Xandra.

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

Winnie	Yen	Xandra
2x4	3x4
	4x3	3x3
8 u	12 u	9 u

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

310 of Winnie's spending = 15 of Yen's spending
310 of Winnie's spending =1x35x3 of Yen's spending
310 of Winnie's spending = 315 of Yen's spending

Winnie : Yen
10 : 15
2 : 3

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

Yen : Xandra
100 : 75
4 : 3

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

Winnie : Yen : Xandra
8 : 12 : 9

(b)

	Winnie	Yen	Xandra
Before	8 u	12 u	9 u
Change		- 3 u
After	8 u	9 u	9 u

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

3 u = 315

1 u = 315 ÷ 3 = 105

Amount that Xandra spent
= 9 u
= 9 x 105
= $945 

Answer(s): (a) 8 : 12 : 9; (b) $945