Three women, Anna, Gillian and Xandra went on a shopping spree. 30% of Anna's spending was equal to ¹₂ of Gillian's spending. Xandra's spending was  25% less than Gillian's. If Gillian spent $63 less, she would spend the same amount of money as Xandra.

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

Anna	Gillian	Xandra
5x4	3x4
	4x3	3x3
20 u	12 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Anna's spending is equal to ¹₂ of Gillian's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Anna's spending = 12 of Gillian's spending
310 of Anna's spending =1x32x3 of Gillian's spending
310 of Anna's spending = 36 of Gillian's spending

Anna : Gillian
10 : 6
5 : 3

Xandra's spending in percent when compared to Gillian's
= 100% - 25%
= 75%

Gillian : Xandra
100 : 75
4 : 3

Gillian's spending is the repeated identity.  Make Gillian's spending the same.  LCM of 3 and 4 is 12.

Anna : Gillian : Xandra
20 : 12 : 9

(b)

	Anna	Gillian	Xandra
Before	20 u	12 u	9 u
Change		- 3 u
After	20 u	9 u	9 u

Additional amount that Gillian would have to spend less to be the same as Xandra
= 12 u - 9 u
= 3 u

3 u = 63

1 u = 63 ÷ 3 = 21

Amount that Xandra spent
= 9 u
= 9 x 21
= $189 

Answer(s): (a) 20 : 12 : 9; (b) $189