Three women, Yoko, Lynn and Risa went on a shopping spree. 30% of Yoko's spending was equal to ¹₂ of Lynn's spending. Risa's spending was  80% less than Lynn's. If Lynn spent $1272 less, she would spend the same amount of money as Risa.

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

Yoko	Lynn	Risa
5x5	3x5
	5x3	1x3
25 u	15 u	3 u

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

310 of Yoko's spending = 12 of Lynn's spending
310 of Yoko's spending =1x32x3 of Lynn's spending
310 of Yoko's spending = 36 of Lynn's spending

Yoko : Lynn
10 : 6
5 : 3

Risa's spending in percent when compared to Lynn's
= 100% - 80%
= 20%

Lynn : Risa
100 : 20
5 : 1

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

Yoko : Lynn : Risa
25 : 15 : 3

(b)

	Yoko	Lynn	Risa
Before	25 u	15 u	3 u
Change		- 12 u
After	25 u	3 u	3 u

Additional amount that Lynn would have to spend less to be the same as Risa
= 15 u - 3 u
= 12 u

12 u = 1272

1 u = 1272 ÷ 12 = 106

Amount that Risa spent
= 3 u
= 3 x 106
= $318 

Answer(s): (a) 25 : 15 : 3; (b) $318