Three women, Xandra, Shannon and Gillian went on a shopping spree. 30% of Xandra's spending was equal to ¹₅ of Shannon's spending. Gillian's spending was  40% more than Shannon's. If Shannon spent another $624, she would spend the same amount of money as Gillian.

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

Xandra	Shannon	Gillian
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

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

310 of Xandra's spending = 15 of Shannon's spending
310 of Xandra's spending =1x35x3 of Shannon's spending
310 of Xandra's spending = 315 of Shannon's spending

Xandra : Shannon
10 : 15
2 : 3

Gillian's spending in percent when compared to Shannon's
= 100% + 40%
= 140%

Shannon : Gillian
100 : 140
5 : 7

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

Xandra : Shannon : Gillian
10 : 15 : 21

(b)

	Xandra	Shannon	Gillian
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Shannon would have to spend to be the same as Gillian
= 21 u - 15 u
= 6 u

6 u = 624

1 u = 624 ÷ 6 = 104

Amount that Xandra spent
= 10 u
= 10 x 104
= $1040 

Answer(s): (a) 10 : 15 : 21; (b) $1040