Three women, Tiffany, Pamela and Zara went on a shopping spree. 30% of Tiffany's spending was equal to ¹₂ of Pamela's spending. Zara's spending was  25% more than Pamela's. If Pamela spent another $285, she would spend the same amount of money as Zara.

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

Tiffany	Pamela	Zara
5x4	3x4
	4x3	5x3
20 u	12 u	15 u

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

310 of Tiffany's spending = 12 of Pamela's spending
310 of Tiffany's spending =1x32x3 of Pamela's spending
310 of Tiffany's spending = 36 of Pamela's spending

Tiffany : Pamela
10 : 6
5 : 3

Zara's spending in percent when compared to Pamela's
= 100% + 25%
= 125%

Pamela : Zara
100 : 125
4 : 5

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

Tiffany : Pamela : Zara
20 : 12 : 15

(b)

	Tiffany	Pamela	Zara
Before	20 u	12 u	15 u
Change		+ 3 u
After	20 u	15 u	15 u

Additional amount that Pamela would have to spend to be the same as Zara
= 15 u - 12 u
= 3 u

3 u = 285

1 u = 285 ÷ 3 = 95

Amount that Tiffany spent
= 20 u
= 20 x 95
= $1900 

Answer(s): (a) 20 : 12 : 15; (b) $1900