Three women, Elyse, Cathy and Xylia went on a shopping spree. 90% of Elyse's spending was equal to ¹₂ of Cathy's spending. Xylia's spending was  60% less than Cathy's. If Cathy spent $2268 less, she would spend the same amount of money as Xylia.

1. Find the ratio of Elyse's spending to Cathy's to Xylia's.
2. How much did Xylia spend?

Elyse	Cathy	Xylia
5x5	9x5
	5x9	2x9
25 u	45 u	18 u

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

910 of Elyse's spending = 12 of Cathy's spending
910 of Elyse's spending =1x92x9 of Cathy's spending
910 of Elyse's spending = 918 of Cathy's spending

Elyse : Cathy
10 : 18
5 : 9

Xylia's spending in percent when compared to Cathy's
= 100% - 60%
= 40%

Cathy : Xylia
100 : 40
5 : 2

Cathy's spending is the repeated identity.  Make Cathy's spending the same.  LCM of 9 and 5 is 45.

Elyse : Cathy : Xylia
25 : 45 : 18

(b)

	Elyse	Cathy	Xylia
Before	25 u	45 u	18 u
Change		- 27 u
After	25 u	18 u	18 u

Additional amount that Cathy would have to spend less to be the same as Xylia
= 45 u - 18 u
= 27 u

27 u = 2268

1 u = 2268 ÷ 27 = 84

Amount that Xylia spent
= 18 u
= 18 x 84
= $1512 

Answer(s): (a) 25 : 45 : 18; (b) $1512