Three women, Risa, Joelle and Zoe went on a shopping spree. 70% of Risa's spending was equal to ¹₂ of Joelle's spending. Zoe's spending was  80% less than Joelle's. If Joelle spent $1568 less, she would spend the same amount of money as Zoe.

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

Risa	Joelle	Zoe
5x5	7x5
	5x7	1x7
25 u	35 u	7 u

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

710 of Risa's spending = 12 of Joelle's spending
710 of Risa's spending =1x72x7 of Joelle's spending
710 of Risa's spending = 714 of Joelle's spending

Risa : Joelle
10 : 14
5 : 7

Zoe's spending in percent when compared to Joelle's
= 100% - 80%
= 20%

Joelle : Zoe
100 : 20
5 : 1

Joelle's spending is the repeated identity.  Make Joelle's spending the same.  LCM of 7 and 5 is 35.

Risa : Joelle : Zoe
25 : 35 : 7

(b)

	Risa	Joelle	Zoe
Before	25 u	35 u	7 u
Change		- 28 u
After	25 u	7 u	7 u

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

28 u = 1568

1 u = 1568 ÷ 28 = 56

Amount that Zoe spent
= 7 u
= 7 x 56
= $392 

Answer(s): (a) 25 : 35 : 7; (b) $392