Three women, Cathy, Yen and Xylia went on a shopping spree. 70% of Cathy's spending was equal to ¹₅ of Yen's spending. Xylia's spending was  70% less than Yen's. If Yen spent $4508 less, she would spend the same amount of money as Xylia.

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

Cathy	Yen	Xylia
2x10	7x10
	10x7	3x7
20 u	70 u	21 u

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

710 of Cathy's spending = 15 of Yen's spending
710 of Cathy's spending =1x75x7 of Yen's spending
710 of Cathy's spending = 735 of Yen's spending

Cathy : Yen
10 : 35
2 : 7

Xylia's spending in percent when compared to Yen's
= 100% - 70%
= 30%

Yen : Xylia
100 : 30
10 : 3

Yen's spending is the repeated identity.  Make Yen's spending the same.  LCM of 7 and 10 is 70.

Cathy : Yen : Xylia
20 : 70 : 21

(b)

	Cathy	Yen	Xylia
Before	20 u	70 u	21 u
Change		- 49 u
After	20 u	21 u	21 u

Additional amount that Yen would have to spend less to be the same as Xylia
= 70 u - 21 u
= 49 u

49 u = 4508

1 u = 4508 ÷ 49 = 92

Amount that Xylia spent
= 21 u
= 21 x 92
= $1932 

Answer(s): (a) 20 : 70 : 21; (b) $1932