Three women, Eva, Rachel and Usha went on a shopping spree. 70% of Eva's spending was equal to ¹₅ of Rachel's spending. Usha's spending was  60% less than Rachel's. If Rachel spent $1722 less, she would spend the same amount of money as Usha.

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

Eva	Rachel	Usha
2x5	7x5
	5x7	2x7
10 u	35 u	14 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Eva's spending is equal to ¹₅ of Rachel's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Eva's spending = 15 of Rachel's spending
710 of Eva's spending =1x75x7 of Rachel's spending
710 of Eva's spending = 735 of Rachel's spending

Eva : Rachel
10 : 35
2 : 7

Usha's spending in percent when compared to Rachel's
= 100% - 60%
= 40%

Rachel : Usha
100 : 40
5 : 2

Rachel's spending is the repeated identity.  Make Rachel's spending the same.  LCM of 7 and 5 is 35.

Eva : Rachel : Usha
10 : 35 : 14

(b)

	Eva	Rachel	Usha
Before	10 u	35 u	14 u
Change		- 21 u
After	10 u	14 u	14 u

Additional amount that Rachel would have to spend less to be the same as Usha
= 35 u - 14 u
= 21 u

21 u = 1722

1 u = 1722 ÷ 21 = 82

Amount that Usha spent
= 14 u
= 14 x 82
= $1148 

Answer(s): (a) 10 : 35 : 14; (b) $1148