Three women, Gem, Julie and Vanessa went on a shopping spree. 30% of Gem's spending was equal to ¹₅ of Julie's spending. Vanessa's spending was  25% less than Julie's. If Julie spent $264 less, she would spend the same amount of money as Vanessa.

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

Gem	Julie	Vanessa
2x4	3x4
	4x3	3x3
8 u	12 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Gem's spending is equal to ¹₅ of Julie's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Gem's spending = 15 of Julie's spending
310 of Gem's spending =1x35x3 of Julie's spending
310 of Gem's spending = 315 of Julie's spending

Gem : Julie
10 : 15
2 : 3

Vanessa's spending in percent when compared to Julie's
= 100% - 25%
= 75%

Julie : Vanessa
100 : 75
4 : 3

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

Gem : Julie : Vanessa
8 : 12 : 9

(b)

	Gem	Julie	Vanessa
Before	8 u	12 u	9 u
Change		- 3 u
After	8 u	9 u	9 u

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

3 u = 264

1 u = 264 ÷ 3 = 88

Amount that Vanessa spent
= 9 u
= 9 x 88
= $792 

Answer(s): (a) 8 : 12 : 9; (b) $792