Three women, Sabrina, Emily and Winnie went on a shopping spree. 30% of Sabrina's spending was equal to ¹₆ of Emily's spending. Winnie's spending was  50% more than Emily's. If Emily spent another $1053, she would spend the same amount of money as Winnie.

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

Sabrina	Emily	Winnie
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Sabrina's spending is equal to ¹₆ of Emily's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Sabrina's spending = 16 of Emily's spending
310 of Sabrina's spending =1x36x3 of Emily's spending
310 of Sabrina's spending = 318 of Emily's spending

Sabrina : Emily
10 : 18
5 : 9

Winnie's spending in percent when compared to Emily's
= 100% + 50%
= 150%

Emily : Winnie
100 : 150
2 : 3

Emily's spending is the repeated identity.  Make Emily's spending the same.  LCM of 9 and 2 is 18.

Sabrina : Emily : Winnie
10 : 18 : 27

(b)

	Sabrina	Emily	Winnie
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

Additional amount that Emily would have to spend to be the same as Winnie
= 27 u - 18 u
= 9 u

9 u = 1053

1 u = 1053 ÷ 9 = 117

Amount that Sabrina spent
= 10 u
= 10 x 117
= $1170 

Answer(s): (a) 10 : 18 : 27; (b) $1170