Three women, Esther, Cindy and Olivia went on a shopping spree. 70% of Esther's spending was equal to ¹₅ of Cindy's spending. Olivia's spending was  60% more than Cindy's. If Cindy spent another $1764, she would spend the same amount of money as Olivia.

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

Esther	Cindy	Olivia
2x5	7x5
	5x7	8x7
10 u	35 u	56 u

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

710 of Esther's spending = 15 of Cindy's spending
710 of Esther's spending =1x75x7 of Cindy's spending
710 of Esther's spending = 735 of Cindy's spending

Esther : Cindy
10 : 35
2 : 7

Olivia's spending in percent when compared to Cindy's
= 100% + 60%
= 160%

Cindy : Olivia
100 : 160
5 : 8

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

Esther : Cindy : Olivia
10 : 35 : 56

(b)

	Esther	Cindy	Olivia
Before	10 u	35 u	56 u
Change		+ 21 u
After	10 u	56 u	56 u

Additional amount that Cindy would have to spend to be the same as Olivia
= 56 u - 35 u
= 21 u

21 u = 1764

1 u = 1764 ÷ 21 = 84

Amount that Esther spent
= 10 u
= 10 x 84
= $840 

Answer(s): (a) 10 : 35 : 56; (b) $840