Three women, Elyse, Hilda and Dana went on a shopping spree. 30% of Elyse's spending was equal to ¹₆ of Hilda's spending. Dana's spending was  60% more than Hilda's. If Hilda spent another $2106, she would spend the same amount of money as Dana.

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

Elyse	Hilda	Dana
5x5	9x5
	5x9	8x9
25 u	45 u	72 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Elyse's spending is equal to ¹₆ of Hilda's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Elyse's spending = 16 of Hilda's spending
310 of Elyse's spending =1x36x3 of Hilda's spending
310 of Elyse's spending = 318 of Hilda's spending

Elyse : Hilda
10 : 18
5 : 9

Dana's spending in percent when compared to Hilda's
= 100% + 60%
= 160%

Hilda : Dana
100 : 160
5 : 8

Hilda's spending is the repeated identity.  Make Hilda's spending the same.  LCM of 9 and 5 is 45.

Elyse : Hilda : Dana
25 : 45 : 72

(b)

	Elyse	Hilda	Dana
Before	25 u	45 u	72 u
Change		+ 27 u
After	25 u	72 u	72 u

Additional amount that Hilda would have to spend to be the same as Dana
= 72 u - 45 u
= 27 u

27 u = 2106

1 u = 2106 ÷ 27 = 78

Amount that Elyse spent
= 25 u
= 25 x 78
= $1950 

Answer(s): (a) 25 : 45 : 72; (b) $1950