Three women, Nora, Xylia and Joelle went on a shopping spree. 30% of Nora's spending was equal to ¹₅ of Xylia's spending. Joelle's spending was  80% less than Xylia's. If Xylia spent $552 less, she would spend the same amount of money as Joelle.

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

Nora	Xylia	Joelle
2x5	3x5
	5x3	1x3
10 u	15 u	3 u

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

310 of Nora's spending = 15 of Xylia's spending
310 of Nora's spending =1x35x3 of Xylia's spending
310 of Nora's spending = 315 of Xylia's spending

Nora : Xylia
10 : 15
2 : 3

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

Xylia : Joelle
100 : 20
5 : 1

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

Nora : Xylia : Joelle
10 : 15 : 3

(b)

	Nora	Xylia	Joelle
Before	10 u	15 u	3 u
Change		- 12 u
After	10 u	3 u	3 u

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

12 u = 552

1 u = 552 ÷ 12 = 46

Amount that Joelle spent
= 3 u
= 3 x 46
= $138 

Answer(s): (a) 10 : 15 : 3; (b) $138