Three women, Zara, Esther and Elyse went on a shopping spree. 90% of Zara's spending was equal to ¹₆ of Esther's spending. Elyse's spending was  80% less than Esther's. If Esther spent $11556 less, she would spend the same amount of money as Elyse.

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

Zara	Esther	Elyse
5x5	27x5
	5x27	1x27
25 u	135 u	27 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Zara's spending is equal to ¹₆ of Esther's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Zara's spending = 16 of Esther's spending
910 of Zara's spending =1x96x9 of Esther's spending
910 of Zara's spending = 954 of Esther's spending

Zara : Esther
10 : 54
5 : 27

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

Esther : Elyse
100 : 20
5 : 1

Esther's spending is the repeated identity.  Make Esther's spending the same.  LCM of 27 and 5 is 135.

Zara : Esther : Elyse
25 : 135 : 27

(b)

	Zara	Esther	Elyse
Before	25 u	135 u	27 u
Change		- 108 u
After	25 u	27 u	27 u

Additional amount that Esther would have to spend less to be the same as Elyse
= 135 u - 27 u
= 108 u

108 u = 11556

1 u = 11556 ÷ 108 = 107

Amount that Elyse spent
= 27 u
= 27 x 107
= $2889 

Answer(s): (a) 25 : 135 : 27; (b) $2889