Three women, Risa, Natalie and Rachel went on a shopping spree. 70% of Risa's spending was equal to ¹₆ of Natalie's spending. Rachel's spending was  25% more than Natalie's. If Natalie spent another $567, she would spend the same amount of money as Rachel.

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

Risa	Natalie	Rachel
5x4	21x4
	4x21	5x21
20 u	84 u	105 u

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

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

Risa : Natalie
10 : 42
5 : 21

Rachel's spending in percent when compared to Natalie's
= 100% + 25%
= 125%

Natalie : Rachel
100 : 125
4 : 5

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

Risa : Natalie : Rachel
20 : 84 : 105

(b)

	Risa	Natalie	Rachel
Before	20 u	84 u	105 u
Change		+ 21 u
After	20 u	105 u	105 u

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

21 u = 567

1 u = 567 ÷ 21 = 27

Amount that Risa spent
= 20 u
= 20 x 27
= $540 

Answer(s): (a) 20 : 84 : 105; (b) $540