Three women, Cindy, Gabby and Yen went on a shopping spree. 70% of Cindy's spending was equal to ¹₂ of Gabby's spending. Yen's spending was  60% more than Gabby's. If Gabby spent another $1449, she would spend the same amount of money as Yen.

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

Cindy	Gabby	Yen
5x5	7x5
	5x7	8x7
25 u	35 u	56 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Cindy's spending is equal to ¹₂ of Gabby's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Cindy's spending = 12 of Gabby's spending
710 of Cindy's spending =1x72x7 of Gabby's spending
710 of Cindy's spending = 714 of Gabby's spending

Cindy : Gabby
10 : 14
5 : 7

Yen's spending in percent when compared to Gabby's
= 100% + 60%
= 160%

Gabby : Yen
100 : 160
5 : 8

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

Cindy : Gabby : Yen
25 : 35 : 56

(b)

	Cindy	Gabby	Yen
Before	25 u	35 u	56 u
Change		+ 21 u
After	25 u	56 u	56 u

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

21 u = 1449

1 u = 1449 ÷ 21 = 69

Amount that Cindy spent
= 25 u
= 25 x 69
= $1725 

Answer(s): (a) 25 : 35 : 56; (b) $1725