Three women, Gwen, Jean and Pamela went on a shopping spree. 30% of Gwen's spending was equal to ¹₅ of Jean's spending. Pamela's spending was  25% more than Jean's. If Jean spent another $318, she would spend the same amount of money as Pamela.

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

Gwen	Jean	Pamela
2x4	3x4
	4x3	5x3
8 u	12 u	15 u

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

310 of Gwen's spending = 15 of Jean's spending
310 of Gwen's spending =1x35x3 of Jean's spending
310 of Gwen's spending = 315 of Jean's spending

Gwen : Jean
10 : 15
2 : 3

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

Jean : Pamela
100 : 125
4 : 5

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

Gwen : Jean : Pamela
8 : 12 : 15

(b)

	Gwen	Jean	Pamela
Before	8 u	12 u	15 u
Change		+ 3 u
After	8 u	15 u	15 u

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

3 u = 318

1 u = 318 ÷ 3 = 106

Amount that Gwen spent
= 8 u
= 8 x 106
= $848 

Answer(s): (a) 8 : 12 : 15; (b) $848