Three women, Min, Raeann and Hilda went on a shopping spree. 30% of Min's spending was equal to ¹₅ of Raeann's spending. Hilda's spending was  50% more than Raeann's. If Raeann spent another $156, she would spend the same amount of money as Hilda.

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

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

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

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

Min : Raeann
10 : 15
2 : 3

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

Raeann : Hilda
100 : 150
2 : 3

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

Min : Raeann : Hilda
4 : 6 : 9

(b)

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

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

3 u = 156

1 u = 156 ÷ 3 = 52

Amount that Min spent
= 4 u
= 4 x 52
= $208 

Answer(s): (a) 4 : 6 : 9; (b) $208