Three women, Dana, Tiffany and Marion went on a shopping spree. 30% of Dana's spending was equal to ¹₆ of Tiffany's spending. Marion's spending was  70% less than Tiffany's. If Tiffany spent $7119 less, she would spend the same amount of money as Marion.

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

Dana	Tiffany	Marion
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

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

310 of Dana's spending = 16 of Tiffany's spending
310 of Dana's spending =1x36x3 of Tiffany's spending
310 of Dana's spending = 318 of Tiffany's spending

Dana : Tiffany
10 : 18
5 : 9

Marion's spending in percent when compared to Tiffany's
= 100% - 70%
= 30%

Tiffany : Marion
100 : 30
10 : 3

Tiffany's spending is the repeated identity.  Make Tiffany's spending the same.  LCM of 9 and 10 is 90.

Dana : Tiffany : Marion
50 : 90 : 27

(b)

	Dana	Tiffany	Marion
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

Additional amount that Tiffany would have to spend less to be the same as Marion
= 90 u - 27 u
= 63 u

63 u = 7119

1 u = 7119 ÷ 63 = 113

Amount that Marion spent
= 27 u
= 27 x 113
= $3051 

Answer(s): (a) 50 : 90 : 27; (b) $3051