Three women, Yen, Nicole and Xandra went on a shopping spree. 30% of Yen's spending was equal to ¹₂ of Nicole's spending. Xandra's spending was  40% more than Nicole's. If Nicole spent another $282, she would spend the same amount of money as Xandra.

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

Yen	Nicole	Xandra
5x5	3x5
	5x3	7x3
25 u	15 u	21 u

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

310 of Yen's spending = 12 of Nicole's spending
310 of Yen's spending =1x32x3 of Nicole's spending
310 of Yen's spending = 36 of Nicole's spending

Yen : Nicole
10 : 6
5 : 3

Xandra's spending in percent when compared to Nicole's
= 100% + 40%
= 140%

Nicole : Xandra
100 : 140
5 : 7

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

Yen : Nicole : Xandra
25 : 15 : 21

(b)

	Yen	Nicole	Xandra
Before	25 u	15 u	21 u
Change		+ 6 u
After	25 u	21 u	21 u

Additional amount that Nicole would have to spend to be the same as Xandra
= 21 u - 15 u
= 6 u

6 u = 282

1 u = 282 ÷ 6 = 47

Amount that Yen spent
= 25 u
= 25 x 47
= $1175 

Answer(s): (a) 25 : 15 : 21; (b) $1175