Three women, Shannon, Penelope and Wendy went on a shopping spree. 30% of Shannon's spending was equal to ¹₂ of Penelope's spending. Wendy's spending was  50% more than Penelope's. If Penelope spent another $72, she would spend the same amount of money as Wendy.

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

Shannon	Penelope	Wendy
5x2	3x2
	2x3	3x3
10 u	6 u	9 u

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

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

Shannon : Penelope
10 : 6
5 : 3

Wendy's spending in percent when compared to Penelope's
= 100% + 50%
= 150%

Penelope : Wendy
100 : 150
2 : 3

Penelope's spending is the repeated identity.  Make Penelope's spending the same.  LCM of 3 and 2 is 6.

Shannon : Penelope : Wendy
10 : 6 : 9

(b)

	Shannon	Penelope	Wendy
Before	10 u	6 u	9 u
Change		+ 3 u
After	10 u	9 u	9 u

Additional amount that Penelope would have to spend to be the same as Wendy
= 9 u - 6 u
= 3 u

3 u = 72

1 u = 72 ÷ 3 = 24

Amount that Shannon spent
= 10 u
= 10 x 24
= $240 

Answer(s): (a) 10 : 6 : 9; (b) $240