Three women, Elyse, Barbara and Zara went on a shopping spree. 30% of Elyse's spending was equal to ¹₆ of Barbara's spending. Zara's spending was  80% less than Barbara's. If Barbara spent $3132 less, she would spend the same amount of money as Zara.

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

Elyse	Barbara	Zara
5x5	9x5
	5x9	1x9
25 u	45 u	9 u

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

310 of Elyse's spending = 16 of Barbara's spending
310 of Elyse's spending =1x36x3 of Barbara's spending
310 of Elyse's spending = 318 of Barbara's spending

Elyse : Barbara
10 : 18
5 : 9

Zara's spending in percent when compared to Barbara's
= 100% - 80%
= 20%

Barbara : Zara
100 : 20
5 : 1

Barbara's spending is the repeated identity.  Make Barbara's spending the same.  LCM of 9 and 5 is 45.

Elyse : Barbara : Zara
25 : 45 : 9

(b)

	Elyse	Barbara	Zara
Before	25 u	45 u	9 u
Change		- 36 u
After	25 u	9 u	9 u

Additional amount that Barbara would have to spend less to be the same as Zara
= 45 u - 9 u
= 36 u

36 u = 3132

1 u = 3132 ÷ 36 = 87

Amount that Zara spent
= 9 u
= 9 x 87
= $783 

Answer(s): (a) 25 : 45 : 9; (b) $783