Three women, Raeann, Hilda and Wendy went on a shopping spree. 30% of Raeann's spending was equal to ¹₅ of Hilda's spending. Wendy's spending was  50% more than Hilda's. If Hilda spent another $162, she would spend the same amount of money as Wendy.

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

Raeann	Hilda	Wendy
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

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

310 of Raeann's spending = 15 of Hilda's spending
310 of Raeann's spending =1x35x3 of Hilda's spending
310 of Raeann's spending = 315 of Hilda's spending

Raeann : Hilda
10 : 15
2 : 3

Wendy's spending in percent when compared to Hilda's
= 100% + 50%
= 150%

Hilda : Wendy
100 : 150
2 : 3

Hilda's spending is the repeated identity.  Make Hilda's spending the same.  LCM of 3 and 2 is 6.

Raeann : Hilda : Wendy
4 : 6 : 9

(b)

	Raeann	Hilda	Wendy
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

Additional amount that Hilda would have to spend to be the same as Wendy
= 9 u - 6 u
= 3 u

3 u = 162

1 u = 162 ÷ 3 = 54

Amount that Raeann spent
= 4 u
= 4 x 54
= $216 

Answer(s): (a) 4 : 6 : 9; (b) $216