Three women, Xandra, Elyse and Linda went on a shopping spree. 30% of Xandra's spending was equal to ¹₆ of Elyse's spending. Linda's spending was  60% more than Elyse's. If Elyse spent another $2268, she would spend the same amount of money as Linda.

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

Xandra	Elyse	Linda
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Xandra's spending is equal to ¹₆ of Elyse's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Xandra's spending = 16 of Elyse's spending
310 of Xandra's spending =1x36x3 of Elyse's spending
310 of Xandra's spending = 318 of Elyse's spending

Xandra : Elyse
10 : 18
5 : 9

Linda's spending in percent when compared to Elyse's
= 100% + 60%
= 160%

Elyse : Linda
100 : 160
5 : 8

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

Xandra : Elyse : Linda
25 : 45 : 72

(b)

	Xandra	Elyse	Linda
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Elyse would have to spend to be the same as Linda
= 72 u - 45 u
= 27 u

27 u = 2268

1 u = 2268 ÷ 27 = 84

Amount that Xandra spent
= 25 u
= 25 x 84
= $2100 

Answer(s): (a) 25 : 45 : 72; (b) $2100