Three women, Jen, Fiona and Xandra went on a shopping spree. 30% of Jen's spending was equal to ¹₅ of Fiona's spending. Xandra's spending was  40% less than Fiona's. If Fiona spent $540 less, she would spend the same amount of money as Xandra.

1. Find the ratio of Jen's spending to Fiona's to Xandra's.
2. How much did Xandra spend?

Jen	Fiona	Xandra
2x5	3x5
	5x3	3x3
10 u	15 u	9 u

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

310 of Jen's spending = 15 of Fiona's spending
310 of Jen's spending =1x35x3 of Fiona's spending
310 of Jen's spending = 315 of Fiona's spending

Jen : Fiona
10 : 15
2 : 3

Xandra's spending in percent when compared to Fiona's
= 100% - 40%
= 60%

Fiona : Xandra
100 : 60
5 : 3

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

Jen : Fiona : Xandra
10 : 15 : 9

(b)

	Jen	Fiona	Xandra
Before	10 u	15 u	9 u
Change		- 6 u
After	10 u	9 u	9 u

Additional amount that Fiona would have to spend less to be the same as Xandra
= 15 u - 9 u
= 6 u

6 u = 540

1 u = 540 ÷ 6 = 90

Amount that Xandra spent
= 9 u
= 9 x 90
= $810 

Answer(s): (a) 10 : 15 : 9; (b) $810