Three women, Emily, Marion and Sabrina went on a shopping spree. 90% of Emily's spending was equal to ¹₅ of Marion's spending. Sabrina's spending was  60% less than Marion's. If Marion spent $1296 less, she would spend the same amount of money as Sabrina.

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

Emily	Marion	Sabrina
2x5	9x5
	5x9	2x9
10 u	45 u	18 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Emily's spending is equal to ¹₅ of Marion's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Emily's spending = 15 of Marion's spending
910 of Emily's spending =1x95x9 of Marion's spending
910 of Emily's spending = 945 of Marion's spending

Emily : Marion
10 : 45
2 : 9

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

Marion : Sabrina
100 : 40
5 : 2

Marion's spending is the repeated identity.  Make Marion's spending the same.  LCM of 9 and 5 is 45.

Emily : Marion : Sabrina
10 : 45 : 18

(b)

	Emily	Marion	Sabrina
Before	10 u	45 u	18 u
Change		- 27 u
After	10 u	18 u	18 u

Additional amount that Marion would have to spend less to be the same as Sabrina
= 45 u - 18 u
= 27 u

27 u = 1296

1 u = 1296 ÷ 27 = 48

Amount that Sabrina spent
= 18 u
= 18 x 48
= $864 

Answer(s): (a) 10 : 45 : 18; (b) $864