Three women, Emily, Gabby and Mary went on a shopping spree. 30% of Emily's spending was equal to ¹₂ of Gabby's spending. Mary's spending was  60% less than Gabby's. If Gabby spent $684 less, she would spend the same amount of money as Mary.

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

Emily	Gabby	Mary
5x5	3x5
	5x3	2x3
25 u	15 u	6 u

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

310 of Emily's spending = 12 of Gabby's spending
310 of Emily's spending =1x32x3 of Gabby's spending
310 of Emily's spending = 36 of Gabby's spending

Emily : Gabby
10 : 6
5 : 3

Mary's spending in percent when compared to Gabby's
= 100% - 60%
= 40%

Gabby : Mary
100 : 40
5 : 2

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

Emily : Gabby : Mary
25 : 15 : 6

(b)

	Emily	Gabby	Mary
Before	25 u	15 u	6 u
Change		- 9 u
After	25 u	6 u	6 u

Additional amount that Gabby would have to spend less to be the same as Mary
= 15 u - 6 u
= 9 u

9 u = 684

1 u = 684 ÷ 9 = 76

Amount that Mary spent
= 6 u
= 6 x 76
= $456 

Answer(s): (a) 25 : 15 : 6; (b) $456