Three women, Kimberly, Roshel and Fiona went on a shopping spree. 30% of Kimberly's spending was equal to ¹₅ of Roshel's spending. Fiona's spending was  50% more than Roshel's. If Roshel spent another $234, she would spend the same amount of money as Fiona.

1. Find the ratio of Kimberly's spending to Roshel's to Fiona's.
2. How much did Kimberly spend?

Kimberly	Roshel	Fiona
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

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

310 of Kimberly's spending = 15 of Roshel's spending
310 of Kimberly's spending =1x35x3 of Roshel's spending
310 of Kimberly's spending = 315 of Roshel's spending

Kimberly : Roshel
10 : 15
2 : 3

Fiona's spending in percent when compared to Roshel's
= 100% + 50%
= 150%

Roshel : Fiona
100 : 150
2 : 3

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

Kimberly : Roshel : Fiona
4 : 6 : 9

(b)

	Kimberly	Roshel	Fiona
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

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

3 u = 234

1 u = 234 ÷ 3 = 78

Amount that Kimberly spent
= 4 u
= 4 x 78
= $312 

Answer(s): (a) 4 : 6 : 9; (b) $312