Three women, Roshel, Kathy and Yen went on a shopping spree. 30% of Roshel's spending was equal to ¹₂ of Kathy's spending. Yen's spending was  60% less than Kathy's. If Kathy spent $540 less, she would spend the same amount of money as Yen.

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

Roshel	Kathy	Yen
5x5	3x5
	5x3	2x3
25 u	15 u	6 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Roshel's spending is equal to ¹₂ of Kathy's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Roshel's spending = 12 of Kathy's spending
310 of Roshel's spending =1x32x3 of Kathy's spending
310 of Roshel's spending = 36 of Kathy's spending

Roshel : Kathy
10 : 6
5 : 3

Yen's spending in percent when compared to Kathy's
= 100% - 60%
= 40%

Kathy : Yen
100 : 40
5 : 2

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

Roshel : Kathy : Yen
25 : 15 : 6

(b)

	Roshel	Kathy	Yen
Before	25 u	15 u	6 u
Change		- 9 u
After	25 u	6 u	6 u

Additional amount that Kathy would have to spend less to be the same as Yen
= 15 u - 6 u
= 9 u

9 u = 540

1 u = 540 ÷ 9 = 60

Amount that Yen spent
= 6 u
= 6 x 60
= $360 

Answer(s): (a) 25 : 15 : 6; (b) $360