Three women, Zara, Risa and Winnie went on a shopping spree. 30% of Zara's spending was equal to ¹₅ of Risa's spending. Winnie's spending was  50% more than Risa's. If Risa spent another $213, she would spend the same amount of money as Winnie.

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

Zara	Risa	Winnie
2x2	3x2
	2x3	3x3
4 u	6 u	9 u

(a)
30%= ³⁰₁₀₀ = ³₁₀
³₁₀ of Zara's spending is equal to ¹₅ of Risa's spending. Make the numerators the same.  LCM of 3 and 1 is 3.

310 of Zara's spending = 15 of Risa's spending
310 of Zara's spending =1x35x3 of Risa's spending
310 of Zara's spending = 315 of Risa's spending

Zara : Risa
10 : 15
2 : 3

Winnie's spending in percent when compared to Risa's
= 100% + 50%
= 150%

Risa : Winnie
100 : 150
2 : 3

Risa's spending is the repeated identity.  Make Risa's spending the same.  LCM of 3 and 2 is 6.

Zara : Risa : Winnie
4 : 6 : 9

(b)

	Zara	Risa	Winnie
Before	4 u	6 u	9 u
Change		+ 3 u
After	4 u	9 u	9 u

Additional amount that Risa would have to spend to be the same as Winnie
= 9 u - 6 u
= 3 u

3 u = 213

1 u = 213 ÷ 3 = 71

Amount that Zara spent
= 4 u
= 4 x 71
= $284 

Answer(s): (a) 4 : 6 : 9; (b) $284