Three women, Rachel, Emily and Irene went on a shopping spree. 30% of Rachel's spending was equal to ¹₆ of Emily's spending. Irene's spending was  50% more than Emily's. If Emily spent another $1017, she would spend the same amount of money as Irene.

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

Rachel	Emily	Irene
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

310 of Rachel's spending = 16 of Emily's spending
310 of Rachel's spending =1x36x3 of Emily's spending
310 of Rachel's spending = 318 of Emily's spending

Rachel : Emily
10 : 18
5 : 9

Irene's spending in percent when compared to Emily's
= 100% + 50%
= 150%

Emily : Irene
100 : 150
2 : 3

Emily's spending is the repeated identity.  Make Emily's spending the same.  LCM of 9 and 2 is 18.

Rachel : Emily : Irene
10 : 18 : 27

(b)

	Rachel	Emily	Irene
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Emily would have to spend to be the same as Irene
= 27 u - 18 u
= 9 u

9 u = 1017

1 u = 1017 ÷ 9 = 113

Amount that Rachel spent
= 10 u
= 10 x 113
= $1130 

Answer(s): (a) 10 : 18 : 27; (b) $1130