Three women, Tiffany, Xandra and Nicole went on a shopping spree. 30% of Tiffany's spending was equal to ¹₂ of Xandra's spending. Nicole's spending was  60% more than Xandra's. If Xandra spent another $522, she would spend the same amount of money as Nicole.

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

Tiffany	Xandra	Nicole
5x5	3x5
	5x3	8x3
25 u	15 u	24 u

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

310 of Tiffany's spending = 12 of Xandra's spending
310 of Tiffany's spending =1x32x3 of Xandra's spending
310 of Tiffany's spending = 36 of Xandra's spending

Tiffany : Xandra
10 : 6
5 : 3

Nicole's spending in percent when compared to Xandra's
= 100% + 60%
= 160%

Xandra : Nicole
100 : 160
5 : 8

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

Tiffany : Xandra : Nicole
25 : 15 : 24

(b)

	Tiffany	Xandra	Nicole
Before	25 u	15 u	24 u
Change		+ 9 u
After	25 u	24 u	24 u

Additional amount that Xandra would have to spend to be the same as Nicole
= 24 u - 15 u
= 9 u

9 u = 522

1 u = 522 ÷ 9 = 58

Amount that Tiffany spent
= 25 u
= 25 x 58
= $1450 

Answer(s): (a) 25 : 15 : 24; (b) $1450