Three women, Nora, Joelle and Nicole went on a shopping spree. 30% of Nora's spending was equal to ¹₂ of Joelle's spending. Nicole's spending was  80% less than Joelle's. If Joelle spent $720 less, she would spend the same amount of money as Nicole.

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

Nora	Joelle	Nicole
5x5	3x5
	5x3	1x3
25 u	15 u	3 u

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

310 of Nora's spending = 12 of Joelle's spending
310 of Nora's spending =1x32x3 of Joelle's spending
310 of Nora's spending = 36 of Joelle's spending

Nora : Joelle
10 : 6
5 : 3

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

Joelle : Nicole
100 : 20
5 : 1

Joelle's spending is the repeated identity.  Make Joelle's spending the same.  LCM of 3 and 5 is 15.

Nora : Joelle : Nicole
25 : 15 : 3

(b)

	Nora	Joelle	Nicole
Before	25 u	15 u	3 u
Change		- 12 u
After	25 u	3 u	3 u

Additional amount that Joelle would have to spend less to be the same as Nicole
= 15 u - 3 u
= 12 u

12 u = 720

1 u = 720 ÷ 12 = 60

Amount that Nicole spent
= 3 u
= 3 x 60
= $180 

Answer(s): (a) 25 : 15 : 3; (b) $180