Three women, Marion, Gem and Jean went on a shopping spree. 30% of Marion's spending was equal to ¹₂ of Gem's spending. Jean's spending was  25% more than Gem's. If Gem spent another $144, she would spend the same amount of money as Jean.

1. Find the ratio of Marion's spending to Gem's to Jean's.
2. How much did Marion spend?

Marion	Gem	Jean
5x4	3x4
	4x3	5x3
20 u	12 u	15 u

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

310 of Marion's spending = 12 of Gem's spending
310 of Marion's spending =1x32x3 of Gem's spending
310 of Marion's spending = 36 of Gem's spending

Marion : Gem
10 : 6
5 : 3

Jean's spending in percent when compared to Gem's
= 100% + 25%
= 125%

Gem : Jean
100 : 125
4 : 5

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

Marion : Gem : Jean
20 : 12 : 15

(b)

	Marion	Gem	Jean
Before	20 u	12 u	15 u
Change		+ 3 u
After	20 u	15 u	15 u

Additional amount that Gem would have to spend to be the same as Jean
= 15 u - 12 u
= 3 u

3 u = 144

1 u = 144 ÷ 3 = 48

Amount that Marion spent
= 20 u
= 20 x 48
= $960 

Answer(s): (a) 20 : 12 : 15; (b) $960