Three women, Betty, Min and Tina went on a shopping spree. 30% of Betty's spending was equal to ¹₅ of Min's spending. Tina's spending was  60% less than Min's. If Min spent $216 less, she would spend the same amount of money as Tina.

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

Betty	Min	Tina
2x5	3x5
	5x3	2x3
10 u	15 u	6 u

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

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

Betty : Min
10 : 15
2 : 3

Tina's spending in percent when compared to Min's
= 100% - 60%
= 40%

Min : Tina
100 : 40
5 : 2

Min's spending is the repeated identity.  Make Min's spending the same.  LCM of 3 and 5 is 15.

Betty : Min : Tina
10 : 15 : 6

(b)

	Betty	Min	Tina
Before	10 u	15 u	6 u
Change		- 9 u
After	10 u	6 u	6 u

Additional amount that Min would have to spend less to be the same as Tina
= 15 u - 6 u
= 9 u

9 u = 216

1 u = 216 ÷ 9 = 24

Amount that Tina spent
= 6 u
= 6 x 24
= $144 

Answer(s): (a) 10 : 15 : 6; (b) $144