Three women, Emma, Elyse and Tammy went on a shopping spree. 30% of Emma's spending was equal to ¹₆ of Elyse's spending. Tammy's spending was  80% less than Elyse's. If Elyse spent $3096 less, she would spend the same amount of money as Tammy.

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

Emma	Elyse	Tammy
5x5	9x5
	5x9	1x9
25 u	45 u	9 u

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

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

Emma : Elyse
10 : 18
5 : 9

Tammy's spending in percent when compared to Elyse's
= 100% - 80%
= 20%

Elyse : Tammy
100 : 20
5 : 1

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

Emma : Elyse : Tammy
25 : 45 : 9

(b)

	Emma	Elyse	Tammy
Before	25 u	45 u	9 u
Change		- 36 u
After	25 u	9 u	9 u

Additional amount that Elyse would have to spend less to be the same as Tammy
= 45 u - 9 u
= 36 u

36 u = 3096

1 u = 3096 ÷ 36 = 86

Amount that Tammy spent
= 9 u
= 9 x 86
= $774 

Answer(s): (a) 25 : 45 : 9; (b) $774