Three women, Shannon, Cindy and Kylie went on a shopping spree. 90% of Shannon's spending was equal to ¹₆ of Cindy's spending. Kylie's spending was  25% more than Cindy's. If Cindy spent another $2133, she would spend the same amount of money as Kylie.

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

Shannon	Cindy	Kylie
5x4	27x4
	4x27	5x27
20 u	108 u	135 u

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

910 of Shannon's spending = 16 of Cindy's spending
910 of Shannon's spending =1x96x9 of Cindy's spending
910 of Shannon's spending = 954 of Cindy's spending

Shannon : Cindy
10 : 54
5 : 27

Kylie's spending in percent when compared to Cindy's
= 100% + 25%
= 125%

Cindy : Kylie
100 : 125
4 : 5

Cindy's spending is the repeated identity.  Make Cindy's spending the same.  LCM of 27 and 4 is 108.

Shannon : Cindy : Kylie
20 : 108 : 135

(b)

	Shannon	Cindy	Kylie
Before	20 u	108 u	135 u
Change		+ 27 u
After	20 u	135 u	135 u

Additional amount that Cindy would have to spend to be the same as Kylie
= 135 u - 108 u
= 27 u

27 u = 2133

1 u = 2133 ÷ 27 = 79

Amount that Shannon spent
= 20 u
= 20 x 79
= $1580 

Answer(s): (a) 20 : 108 : 135; (b) $1580