Three women, Raeann, Betty and Pamela went on a shopping spree. 90% of Raeann's spending was equal to ¹₂ of Betty's spending. Pamela's spending was  50% more than Betty's. If Betty spent another $1062, she would spend the same amount of money as Pamela.

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

Raeann	Betty	Pamela
5x2	9x2
	2x9	3x9
10 u	18 u	27 u

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

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

Raeann : Betty
10 : 18
5 : 9

Pamela's spending in percent when compared to Betty's
= 100% + 50%
= 150%

Betty : Pamela
100 : 150
2 : 3

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

Raeann : Betty : Pamela
10 : 18 : 27

(b)

	Raeann	Betty	Pamela
Before	10 u	18 u	27 u
Change		+ 9 u
After	10 u	27 u	27 u

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

9 u = 1062

1 u = 1062 ÷ 9 = 118

Amount that Raeann spent
= 10 u
= 10 x 118
= $1180 

Answer(s): (a) 10 : 18 : 27; (b) $1180