Three women, Risa, Linda and Tiffany went on a shopping spree. 70% of Risa's spending was equal to ¹₆ of Linda's spending. Tiffany's spending was  25% more than Linda's. If Linda spent another $420, she would spend the same amount of money as Tiffany.

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

Risa	Linda	Tiffany
5x4	21x4
	4x21	5x21
20 u	84 u	105 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Risa's spending is equal to ¹₆ of Linda's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Risa's spending = 16 of Linda's spending
710 of Risa's spending =1x76x7 of Linda's spending
710 of Risa's spending = 742 of Linda's spending

Risa : Linda
10 : 42
5 : 21

Tiffany's spending in percent when compared to Linda's
= 100% + 25%
= 125%

Linda : Tiffany
100 : 125
4 : 5

Linda's spending is the repeated identity.  Make Linda's spending the same.  LCM of 21 and 4 is 84.

Risa : Linda : Tiffany
20 : 84 : 105

(b)

	Risa	Linda	Tiffany
Before	20 u	84 u	105 u
Change		+ 21 u
After	20 u	105 u	105 u

Additional amount that Linda would have to spend to be the same as Tiffany
= 105 u - 84 u
= 21 u

21 u = 420

1 u = 420 ÷ 21 = 20

Amount that Risa spent
= 20 u
= 20 x 20
= $400 

Answer(s): (a) 20 : 84 : 105; (b) $400