Three women, Jen, Tina and Tiffany went on a shopping spree. 30% of Jen's spending was equal to ¹₂ of Tina's spending. Tiffany's spending was  70% less than Tina's. If Tina spent $1092 less, she would spend the same amount of money as Tiffany.

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

Jen	Tina	Tiffany
5x10	3x10
	10x3	3x3
50 u	30 u	9 u

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

310 of Jen's spending = 12 of Tina's spending
310 of Jen's spending =1x32x3 of Tina's spending
310 of Jen's spending = 36 of Tina's spending

Jen : Tina
10 : 6
5 : 3

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

Tina : Tiffany
100 : 30
10 : 3

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 3 and 10 is 30.

Jen : Tina : Tiffany
50 : 30 : 9

(b)

	Jen	Tina	Tiffany
Before	50 u	30 u	9 u
Change		- 21 u
After	50 u	9 u	9 u

Additional amount that Tina would have to spend less to be the same as Tiffany
= 30 u - 9 u
= 21 u

21 u = 1092

1 u = 1092 ÷ 21 = 52

Amount that Tiffany spent
= 9 u
= 9 x 52
= $468 

Answer(s): (a) 50 : 30 : 9; (b) $468