Three women, Xandra, Fiona and Shannon went on a shopping spree. 70% of Xandra's spending was equal to ¹₂ of Fiona's spending. Shannon's spending was  40% less than Fiona's. If Fiona spent $1218 less, she would spend the same amount of money as Shannon.

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

Xandra	Fiona	Shannon
5x5	7x5
	5x7	3x7
25 u	35 u	21 u

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

710 of Xandra's spending = 12 of Fiona's spending
710 of Xandra's spending =1x72x7 of Fiona's spending
710 of Xandra's spending = 714 of Fiona's spending

Xandra : Fiona
10 : 14
5 : 7

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

Fiona : Shannon
100 : 60
5 : 3

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

Xandra : Fiona : Shannon
25 : 35 : 21

(b)

	Xandra	Fiona	Shannon
Before	25 u	35 u	21 u
Change		- 14 u
After	25 u	21 u	21 u

Additional amount that Fiona would have to spend less to be the same as Shannon
= 35 u - 21 u
= 14 u

14 u = 1218

1 u = 1218 ÷ 14 = 87

Amount that Shannon spent
= 21 u
= 21 x 87
= $1827 

Answer(s): (a) 25 : 35 : 21; (b) $1827