Three women, Xandra, Tiffany and Cindy went on a shopping spree. 30% of Xandra's spending was equal to ¹₅ of Tiffany's spending. Cindy's spending was  25% more than Tiffany's. If Tiffany spent another $96, she would spend the same amount of money as Cindy.

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

Xandra	Tiffany	Cindy
2x4	3x4
	4x3	5x3
8 u	12 u	15 u

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

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

Xandra : Tiffany
10 : 15
2 : 3

Cindy's spending in percent when compared to Tiffany's
= 100% + 25%
= 125%

Tiffany : Cindy
100 : 125
4 : 5

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

Xandra : Tiffany : Cindy
8 : 12 : 15

(b)

	Xandra	Tiffany	Cindy
Before	8 u	12 u	15 u
Change		+ 3 u
After	8 u	15 u	15 u

Additional amount that Tiffany would have to spend to be the same as Cindy
= 15 u - 12 u
= 3 u

3 u = 96

1 u = 96 ÷ 3 = 32

Amount that Xandra spent
= 8 u
= 8 x 32
= $256 

Answer(s): (a) 8 : 12 : 15; (b) $256