Three women, Elyse, Olivia and Marion went on a shopping spree. 30% of Elyse's spending was equal to ¹₂ of Olivia's spending. Marion's spending was  50% more than Olivia's. If Olivia spent another $99, she would spend the same amount of money as Marion.

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

Elyse	Olivia	Marion
5x2	3x2
	2x3	3x3
10 u	6 u	9 u

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

310 of Elyse's spending = 12 of Olivia's spending
310 of Elyse's spending =1x32x3 of Olivia's spending
310 of Elyse's spending = 36 of Olivia's spending

Elyse : Olivia
10 : 6
5 : 3

Marion's spending in percent when compared to Olivia's
= 100% + 50%
= 150%

Olivia : Marion
100 : 150
2 : 3

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

Elyse : Olivia : Marion
10 : 6 : 9

(b)

	Elyse	Olivia	Marion
Before	10 u	6 u	9 u
Change		+ 3 u
After	10 u	9 u	9 u

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

3 u = 99

1 u = 99 ÷ 3 = 33

Amount that Elyse spent
= 10 u
= 10 x 33
= $330 

Answer(s): (a) 10 : 6 : 9; (b) $330