Three women, Tina, Fanny and Julie went on a shopping spree. 30% of Tina's spending was equal to ¹₅ of Fanny's spending. Julie's spending was  50% more than Fanny's. If Fanny spent another $198, she would spend the same amount of money as Julie.

1. Find the ratio of Tina's spending to Fanny's to Julie's.
2. How much did Tina spend?

Tina	Fanny	Julie
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

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

310 of Tina's spending = 15 of Fanny's spending
310 of Tina's spending =1x35x3 of Fanny's spending
310 of Tina's spending = 315 of Fanny's spending

Tina : Fanny
10 : 15
2 : 3

Julie's spending in percent when compared to Fanny's
= 100% + 50%
= 150%

Fanny : Julie
100 : 150
2 : 3

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

Tina : Fanny : Julie
4 : 6 : 9

(b)

	Tina	Fanny	Julie
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

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

3 u = 198

1 u = 198 ÷ 3 = 66

Amount that Tina spent
= 4 u
= 4 x 66
= $264 

Answer(s): (a) 4 : 6 : 9; (b) $264