Three women, Hilda, Betty and Dana went on a shopping spree. 30% of Hilda's spending was equal to ¹₂ of Betty's spending. Dana's spending was  25% less than Betty's. If Betty spent $216 less, she would spend the same amount of money as Dana.

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

Hilda	Betty	Dana
5x4	3x4
	4x3	3x3
20 u	12 u	9 u

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

310 of Hilda's spending = 12 of Betty's spending
310 of Hilda's spending =1x32x3 of Betty's spending
310 of Hilda's spending = 36 of Betty's spending

Hilda : Betty
10 : 6
5 : 3

Dana's spending in percent when compared to Betty's
= 100% - 25%
= 75%

Betty : Dana
100 : 75
4 : 3

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

Hilda : Betty : Dana
20 : 12 : 9

(b)

	Hilda	Betty	Dana
Before	20 u	12 u	9 u
Change		- 3 u
After	20 u	9 u	9 u

Additional amount that Betty would have to spend less to be the same as Dana
= 12 u - 9 u
= 3 u

3 u = 216

1 u = 216 ÷ 3 = 72

Amount that Dana spent
= 9 u
= 9 x 72
= $648 

Answer(s): (a) 20 : 12 : 9; (b) $648