Three women, Winnie, Esther and Gem went on a shopping spree. 30% of Winnie's spending was equal to ¹₅ of Esther's spending. Gem's spending was  60% more than Esther's. If Esther spent another $567, she would spend the same amount of money as Gem.

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

Winnie	Esther	Gem
2x5	3x5
	5x3	8x3
10 u	15 u	24 u

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

310 of Winnie's spending = 15 of Esther's spending
310 of Winnie's spending =1x35x3 of Esther's spending
310 of Winnie's spending = 315 of Esther's spending

Winnie : Esther
10 : 15
2 : 3

Gem's spending in percent when compared to Esther's
= 100% + 60%
= 160%

Esther : Gem
100 : 160
5 : 8

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

Winnie : Esther : Gem
10 : 15 : 24

(b)

	Winnie	Esther	Gem
Before	10 u	15 u	24 u
Change		+ 9 u
After	10 u	24 u	24 u

Additional amount that Esther would have to spend to be the same as Gem
= 24 u - 15 u
= 9 u

9 u = 567

1 u = 567 ÷ 9 = 63

Amount that Winnie spent
= 10 u
= 10 x 63
= $630 

Answer(s): (a) 10 : 15 : 24; (b) $630