Three women, Xylia, Gem and Mary went on a shopping spree. 30% of Xylia's spending was equal to ¹₂ of Gem's spending. Mary's spending was  25% less than Gem's. If Gem spent $111 less, she would spend the same amount of money as Mary.

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

Xylia	Gem	Mary
5x4	3x4
	4x3	3x3
20 u	12 u	9 u

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

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

Xylia : Gem
10 : 6
5 : 3

Mary's spending in percent when compared to Gem's
= 100% - 25%
= 75%

Gem : Mary
100 : 75
4 : 3

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

Xylia : Gem : Mary
20 : 12 : 9

(b)

	Xylia	Gem	Mary
Before	20 u	12 u	9 u
Change		- 3 u
After	20 u	9 u	9 u

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

3 u = 111

1 u = 111 ÷ 3 = 37

Amount that Mary spent
= 9 u
= 9 x 37
= $333 

Answer(s): (a) 20 : 12 : 9; (b) $333