Three women, Xuan, Kylie and Wendy went on a shopping spree. 30% of Xuan's spending was equal to ¹₂ of Kylie's spending. Wendy's spending was  40% more than Kylie's. If Kylie spent another $258, she would spend the same amount of money as Wendy.

1. Find the ratio of Xuan's spending to Kylie's to Wendy's.
2. How much did Xuan spend?

Xuan	Kylie	Wendy
5x5	3x5
	5x3	7x3
25 u	15 u	21 u

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

310 of Xuan's spending = 12 of Kylie's spending
310 of Xuan's spending =1x32x3 of Kylie's spending
310 of Xuan's spending = 36 of Kylie's spending

Xuan : Kylie
10 : 6
5 : 3

Wendy's spending in percent when compared to Kylie's
= 100% + 40%
= 140%

Kylie : Wendy
100 : 140
5 : 7

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

Xuan : Kylie : Wendy
25 : 15 : 21

(b)

	Xuan	Kylie	Wendy
Before	25 u	15 u	21 u
Change		+ 6 u
After	25 u	21 u	21 u

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

6 u = 258

1 u = 258 ÷ 6 = 43

Amount that Xuan spent
= 25 u
= 25 x 43
= $1075 

Answer(s): (a) 25 : 15 : 21; (b) $1075