Three women, Xandra, Sabrina and Marion went on a shopping spree. 70% of Xandra's spending was equal to ¹₆ of Sabrina's spending. Marion's spending was  60% less than Sabrina's. If Sabrina spent $4977 less, she would spend the same amount of money as Marion.

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

Xandra	Sabrina	Marion
5x5	21x5
	5x21	2x21
25 u	105 u	42 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Xandra's spending is equal to ¹₆ of Sabrina's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Xandra's spending = 16 of Sabrina's spending
710 of Xandra's spending =1x76x7 of Sabrina's spending
710 of Xandra's spending = 742 of Sabrina's spending

Xandra : Sabrina
10 : 42
5 : 21

Marion's spending in percent when compared to Sabrina's
= 100% - 60%
= 40%

Sabrina : Marion
100 : 40
5 : 2

Sabrina's spending is the repeated identity.  Make Sabrina's spending the same.  LCM of 21 and 5 is 105.

Xandra : Sabrina : Marion
25 : 105 : 42

(b)

	Xandra	Sabrina	Marion
Before	25 u	105 u	42 u
Change		- 63 u
After	25 u	42 u	42 u

Additional amount that Sabrina would have to spend less to be the same as Marion
= 105 u - 42 u
= 63 u

63 u = 4977

1 u = 4977 ÷ 63 = 79

Amount that Marion spent
= 42 u
= 42 x 79
= $3318 

Answer(s): (a) 25 : 105 : 42; (b) $3318