Three women, Raeann, Diana and Winnie went on a shopping spree. 90% of Raeann's spending was equal to ¹₂ of Diana's spending. Winnie's spending was  50% more than Diana's. If Diana spent another $1080, she would spend the same amount of money as Winnie.

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

Raeann	Diana	Winnie
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

910 of Raeann's spending = 12 of Diana's spending
910 of Raeann's spending =1x92x9 of Diana's spending
910 of Raeann's spending = 918 of Diana's spending

Raeann : Diana
10 : 18
5 : 9

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

Diana : Winnie
100 : 150
2 : 3

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

Raeann : Diana : Winnie
10 : 18 : 27

(b)

	Raeann	Diana	Winnie
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

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

9 u = 1080

1 u = 1080 ÷ 9 = 120

Amount that Raeann spent
= 10 u
= 10 x 120
= $1200 

Answer(s): (a) 10 : 18 : 27; (b) $1200