Three women, Julie, Nora and Zoe went on a shopping spree. 90% of Julie's spending was equal to ¹₅ of Nora's spending. Zoe's spending was  80% less than Nora's. If Nora spent $2736 less, she would spend the same amount of money as Zoe.

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

Julie	Nora	Zoe
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Julie's spending is equal to ¹₅ of Nora's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Julie's spending = 15 of Nora's spending
910 of Julie's spending =1x95x9 of Nora's spending
910 of Julie's spending = 945 of Nora's spending

Julie : Nora
10 : 45
2 : 9

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

Nora : Zoe
100 : 20
5 : 1

Nora's spending is the repeated identity.  Make Nora's spending the same.  LCM of 9 and 5 is 45.

Julie : Nora : Zoe
10 : 45 : 9

(b)

	Julie	Nora	Zoe
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

Additional amount that Nora would have to spend less to be the same as Zoe
= 45 u - 9 u
= 36 u

36 u = 2736

1 u = 2736 ÷ 36 = 76

Amount that Zoe spent
= 9 u
= 9 x 76
= $684 

Answer(s): (a) 10 : 45 : 9; (b) $684