Three women, Julie, Irene and Usha went on a shopping spree. 70% of Julie's spending was equal to ¹₅ of Irene's spending. Usha's spending was  80% less than Irene's. If Irene spent $2296 less, she would spend the same amount of money as Usha.

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

Julie	Irene	Usha
2x5	7x5
	5x7	1x7
10 u	35 u	7 u

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

710 of Julie's spending = 15 of Irene's spending
710 of Julie's spending =1x75x7 of Irene's spending
710 of Julie's spending = 735 of Irene's spending

Julie : Irene
10 : 35
2 : 7

Usha's spending in percent when compared to Irene's
= 100% - 80%
= 20%

Irene : Usha
100 : 20
5 : 1

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

Julie : Irene : Usha
10 : 35 : 7

(b)

	Julie	Irene	Usha
Before	10 u	35 u	7 u
Change		- 28 u
After	10 u	7 u	7 u

Additional amount that Irene would have to spend less to be the same as Usha
= 35 u - 7 u
= 28 u

28 u = 2296

1 u = 2296 ÷ 28 = 82

Amount that Usha spent
= 7 u
= 7 x 82
= $574 

Answer(s): (a) 10 : 35 : 7; (b) $574