Three women, Kathy, Irene and Esther went on a shopping spree. 70% of Kathy's spending was equal to ¹₆ of Irene's spending. Esther's spending was  80% less than Irene's. If Irene spent $9072 less, she would spend the same amount of money as Esther.

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

Kathy	Irene	Esther
5x5	21x5
	5x21	1x21
25 u	105 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Kathy's spending is equal to ¹₆ of Irene's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Kathy's spending = 16 of Irene's spending
710 of Kathy's spending =1x76x7 of Irene's spending
710 of Kathy's spending = 742 of Irene's spending

Kathy : Irene
10 : 42
5 : 21

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

Irene : Esther
100 : 20
5 : 1

Irene's spending is the repeated identity.  Make Irene's spending the same.  LCM of 21 and 5 is 105.

Kathy : Irene : Esther
25 : 105 : 21

(b)

	Kathy	Irene	Esther
Before	25 u	105 u	21 u
Change		- 84 u
After	25 u	21 u	21 u

Additional amount that Irene would have to spend less to be the same as Esther
= 105 u - 21 u
= 84 u

84 u = 9072

1 u = 9072 ÷ 84 = 108

Amount that Esther spent
= 21 u
= 21 x 108
= $2268 

Answer(s): (a) 25 : 105 : 21; (b) $2268