Three women, Xuan, Fiona and Wendy went on a shopping spree. 90% of Xuan's spending was equal to ¹₂ of Fiona's spending. Wendy's spending was  25% more than Fiona's. If Fiona spent another $252, she would spend the same amount of money as Wendy.

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

Xuan	Fiona	Wendy
5x4	9x4
	4x9	5x9
20 u	36 u	45 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Xuan's spending is equal to ¹₂ of Fiona's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Xuan's spending = 12 of Fiona's spending
910 of Xuan's spending =1x92x9 of Fiona's spending
910 of Xuan's spending = 918 of Fiona's spending

Xuan : Fiona
10 : 18
5 : 9

Wendy's spending in percent when compared to Fiona's
= 100% + 25%
= 125%

Fiona : Wendy
100 : 125
4 : 5

Fiona's spending is the repeated identity.  Make Fiona's spending the same.  LCM of 9 and 4 is 36.

Xuan : Fiona : Wendy
20 : 36 : 45

(b)

	Xuan	Fiona	Wendy
Before	20 u	36 u	45 u
Change		+ 9 u
After	20 u	45 u	45 u

Additional amount that Fiona would have to spend to be the same as Wendy
= 45 u - 36 u
= 9 u

9 u = 252

1 u = 252 ÷ 9 = 28

Amount that Xuan spent
= 20 u
= 20 x 28
= $560 

Answer(s): (a) 20 : 36 : 45; (b) $560