Three women, Esther, Tina and Ivory went on a shopping spree. 30% of Esther's spending was equal to ¹₅ of Tina's spending. Ivory's spending was  25% more than Tina's. If Tina spent another $99, she would spend the same amount of money as Ivory.

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

Esther	Tina	Ivory
2x4	3x4
	4x3	5x3
8 u	12 u	15 u

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

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

Esther : Tina
10 : 15
2 : 3

Ivory's spending in percent when compared to Tina's
= 100% + 25%
= 125%

Tina : Ivory
100 : 125
4 : 5

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 3 and 4 is 12.

Esther : Tina : Ivory
8 : 12 : 15

(b)

	Esther	Tina	Ivory
Before	8 u	12 u	15 u
Change		+ 3 u
After	8 u	15 u	15 u

Additional amount that Tina would have to spend to be the same as Ivory
= 15 u - 12 u
= 3 u

3 u = 99

1 u = 99 ÷ 3 = 33

Amount that Esther spent
= 8 u
= 8 x 33
= $264 

Answer(s): (a) 8 : 12 : 15; (b) $264