Three women, Gwen, Zoe and Julie went on a shopping spree. 70% of Gwen's spending was equal to ¹₂ of Zoe's spending. Julie's spending was  25% more than Zoe's. If Zoe spent another $469, she would spend the same amount of money as Julie.

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

Gwen	Zoe	Julie
5x4	7x4
	4x7	5x7
20 u	28 u	35 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Gwen's spending is equal to ¹₂ of Zoe's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Gwen's spending = 12 of Zoe's spending
710 of Gwen's spending =1x72x7 of Zoe's spending
710 of Gwen's spending = 714 of Zoe's spending

Gwen : Zoe
10 : 14
5 : 7

Julie's spending in percent when compared to Zoe's
= 100% + 25%
= 125%

Zoe : Julie
100 : 125
4 : 5

Zoe's spending is the repeated identity.  Make Zoe's spending the same.  LCM of 7 and 4 is 28.

Gwen : Zoe : Julie
20 : 28 : 35

(b)

	Gwen	Zoe	Julie
Before	20 u	28 u	35 u
Change		+ 7 u
After	20 u	35 u	35 u

Additional amount that Zoe would have to spend to be the same as Julie
= 35 u - 28 u
= 7 u

7 u = 469

1 u = 469 ÷ 7 = 67

Amount that Gwen spent
= 20 u
= 20 x 67
= $1340 

Answer(s): (a) 20 : 28 : 35; (b) $1340