Three women, Penelope, Barbara and Risa went on a shopping spree. 30% of Penelope's spending was equal to ¹₂ of Barbara's spending. Risa's spending was  25% less than Barbara's. If Barbara spent $210 less, she would spend the same amount of money as Risa.

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

Penelope	Barbara	Risa
5x4	3x4
	4x3	3x3
20 u	12 u	9 u

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

310 of Penelope's spending = 12 of Barbara's spending
310 of Penelope's spending =1x32x3 of Barbara's spending
310 of Penelope's spending = 36 of Barbara's spending

Penelope : Barbara
10 : 6
5 : 3

Risa's spending in percent when compared to Barbara's
= 100% - 25%
= 75%

Barbara : Risa
100 : 75
4 : 3

Barbara's spending is the repeated identity.  Make Barbara's spending the same.  LCM of 3 and 4 is 12.

Penelope : Barbara : Risa
20 : 12 : 9

(b)

	Penelope	Barbara	Risa
Before	20 u	12 u	9 u
Change		- 3 u
After	20 u	9 u	9 u

Additional amount that Barbara would have to spend less to be the same as Risa
= 12 u - 9 u
= 3 u

3 u = 210

1 u = 210 ÷ 3 = 70

Amount that Risa spent
= 9 u
= 9 x 70
= $630 

Answer(s): (a) 20 : 12 : 9; (b) $630