Three women, Mary, Tina and Tiffany went on a shopping spree. 30% of Mary's spending was equal to ¹₂ of Tina's spending. Tiffany's spending was  25% more than Tina's. If Tina spent another $237, she would spend the same amount of money as Tiffany.

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

Mary	Tina	Tiffany
5x4	3x4
	4x3	5x3
20 u	12 u	15 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Mary's spending is equal to ¹₂ of Tina's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Mary's spending = 12 of Tina's spending
310 of Mary's spending =1x32x3 of Tina's spending
310 of Mary's spending = 36 of Tina's spending

Mary : Tina
10 : 6
5 : 3

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

Tina : Tiffany
100 : 125
4 : 5

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

Mary : Tina : Tiffany
20 : 12 : 15

(b)

	Mary	Tina	Tiffany
Before	20 u	12 u	15 u
Change		+ 3 u
After	20 u	15 u	15 u

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

3 u = 237

1 u = 237 ÷ 3 = 79

Amount that Mary spent
= 20 u
= 20 x 79
= $1580 

Answer(s): (a) 20 : 12 : 15; (b) $1580