Three women, Tina, Min and Cathy went on a shopping spree. 30% of Tina's spending was equal to ¹₅ of Min's spending. Cathy's spending was  25% more than Min's. If Min spent another $357, she would spend the same amount of money as Cathy.

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

Tina	Min	Cathy
2x4	3x4
	4x3	5x3
8 u	12 u	15 u

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

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

Tina : Min
10 : 15
2 : 3

Cathy's spending in percent when compared to Min's
= 100% + 25%
= 125%

Min : Cathy
100 : 125
4 : 5

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

Tina : Min : Cathy
8 : 12 : 15

(b)

	Tina	Min	Cathy
Before	8 u	12 u	15 u
Change		+ 3 u
After	8 u	15 u	15 u

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

3 u = 357

1 u = 357 ÷ 3 = 119

Amount that Tina spent
= 8 u
= 8 x 119
= $952 

Answer(s): (a) 8 : 12 : 15; (b) $952