Three women, Shannon, Olivia and Xandra went on a shopping spree. 70% of Shannon's spending was equal to ¹₂ of Olivia's spending. Xandra's spending was  80% less than Olivia's. If Olivia spent $924 less, she would spend the same amount of money as Xandra.

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

Shannon	Olivia	Xandra
5x5	7x5
	5x7	1x7
25 u	35 u	7 u

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

710 of Shannon's spending = 12 of Olivia's spending
710 of Shannon's spending =1x72x7 of Olivia's spending
710 of Shannon's spending = 714 of Olivia's spending

Shannon : Olivia
10 : 14
5 : 7

Xandra's spending in percent when compared to Olivia's
= 100% - 80%
= 20%

Olivia : Xandra
100 : 20
5 : 1

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

Shannon : Olivia : Xandra
25 : 35 : 7

(b)

	Shannon	Olivia	Xandra
Before	25 u	35 u	7 u
Change		- 28 u
After	25 u	7 u	7 u

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

28 u = 924

1 u = 924 ÷ 28 = 33

Amount that Xandra spent
= 7 u
= 7 x 33
= $231 

Answer(s): (a) 25 : 35 : 7; (b) $231