Three women, Winnie, Wendy and Hazel went on a shopping spree. 90% of Winnie's spending was equal to ¹₂ of Wendy's spending. Hazel's spending was  60% more than Wendy's. If Wendy spent another $3051, she would spend the same amount of money as Hazel.

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

Winnie	Wendy	Hazel
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Winnie's spending is equal to ¹₂ of Wendy's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Winnie's spending = 12 of Wendy's spending
910 of Winnie's spending =1x92x9 of Wendy's spending
910 of Winnie's spending = 918 of Wendy's spending

Winnie : Wendy
10 : 18
5 : 9

Hazel's spending in percent when compared to Wendy's
= 100% + 60%
= 160%

Wendy : Hazel
100 : 160
5 : 8

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

Winnie : Wendy : Hazel
25 : 45 : 72

(b)

	Winnie	Wendy	Hazel
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Wendy would have to spend to be the same as Hazel
= 72 u - 45 u
= 27 u

27 u = 3051

1 u = 3051 ÷ 27 = 113

Amount that Winnie spent
= 25 u
= 25 x 113
= $2825 

Answer(s): (a) 25 : 45 : 72; (b) $2825