Three women, Cindy, Lynn and Gem went on a shopping spree. 30% of Cindy's spending was equal to ¹₆ of Lynn's spending. Gem's spending was  60% more than Lynn's. If Lynn spent another $3186, she would spend the same amount of money as Gem.

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

Cindy	Lynn	Gem
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

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

310 of Cindy's spending = 16 of Lynn's spending
310 of Cindy's spending =1x36x3 of Lynn's spending
310 of Cindy's spending = 318 of Lynn's spending

Cindy : Lynn
10 : 18
5 : 9

Gem's spending in percent when compared to Lynn's
= 100% + 60%
= 160%

Lynn : Gem
100 : 160
5 : 8

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

Cindy : Lynn : Gem
25 : 45 : 72

(b)

	Cindy	Lynn	Gem
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Lynn would have to spend to be the same as Gem
= 72 u - 45 u
= 27 u

27 u = 3186

1 u = 3186 ÷ 27 = 118

Amount that Cindy spent
= 25 u
= 25 x 118
= $2950 

Answer(s): (a) 25 : 45 : 72; (b) $2950