Three women, Cathy, Cindy and Xylia went on a shopping spree. 30% of Cathy's spending was equal to ¹₅ of Cindy's spending. Xylia's spending was  40% more than Cindy's. If Cindy spent another $678, she would spend the same amount of money as Xylia.

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

Cathy	Cindy	Xylia
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Cathy's spending is equal to ¹₅ of Cindy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Cathy's spending = 15 of Cindy's spending
310 of Cathy's spending =1x35x3 of Cindy's spending
310 of Cathy's spending = 315 of Cindy's spending

Cathy : Cindy
10 : 15
2 : 3

Xylia's spending in percent when compared to Cindy's
= 100% + 40%
= 140%

Cindy : Xylia
100 : 140
5 : 7

Cindy's spending is the repeated identity.  Make Cindy's spending the same.  LCM of 3 and 5 is 15.

Cathy : Cindy : Xylia
10 : 15 : 21

(b)

	Cathy	Cindy	Xylia
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Cindy would have to spend to be the same as Xylia
= 21 u - 15 u
= 6 u

6 u = 678

1 u = 678 ÷ 6 = 113

Amount that Cathy spent
= 10 u
= 10 x 113
= $1130 

Answer(s): (a) 10 : 15 : 21; (b) $1130