Three women, Wendy, Irene and Elyse went on a shopping spree. 30% of Wendy's spending was equal to ¹₆ of Irene's spending. Elyse's spending was  70% less than Irene's. If Irene spent $6363 less, she would spend the same amount of money as Elyse.

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

Wendy	Irene	Elyse
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

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

310 of Wendy's spending = 16 of Irene's spending
310 of Wendy's spending =1x36x3 of Irene's spending
310 of Wendy's spending = 318 of Irene's spending

Wendy : Irene
10 : 18
5 : 9

Elyse's spending in percent when compared to Irene's
= 100% - 70%
= 30%

Irene : Elyse
100 : 30
10 : 3

Irene's spending is the repeated identity.  Make Irene's spending the same.  LCM of 9 and 10 is 90.

Wendy : Irene : Elyse
50 : 90 : 27

(b)

	Wendy	Irene	Elyse
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

Additional amount that Irene would have to spend less to be the same as Elyse
= 90 u - 27 u
= 63 u

63 u = 6363

1 u = 6363 ÷ 63 = 101

Amount that Elyse spent
= 27 u
= 27 x 101
= $2727 

Answer(s): (a) 50 : 90 : 27; (b) $2727