Three women, Julie, Roshel and Zara went on a shopping spree. 30% of Julie's spending was equal to ¹₅ of Roshel's spending. Zara's spending was  40% more than Roshel's. If Roshel spent another $210, she would spend the same amount of money as Zara.

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

Julie	Roshel	Zara
2x5	3x5
	5x3	7x3
10 u	15 u	21 u

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

310 of Julie's spending = 15 of Roshel's spending
310 of Julie's spending =1x35x3 of Roshel's spending
310 of Julie's spending = 315 of Roshel's spending

Julie : Roshel
10 : 15
2 : 3

Zara's spending in percent when compared to Roshel's
= 100% + 40%
= 140%

Roshel : Zara
100 : 140
5 : 7

Roshel's spending is the repeated identity.  Make Roshel's spending the same.  LCM of 3 and 5 is 15.

Julie : Roshel : Zara
10 : 15 : 21

(b)

	Julie	Roshel	Zara
Before	10 u	15 u	21 u
Change		+ 6 u
After	10 u	21 u	21 u

Additional amount that Roshel would have to spend to be the same as Zara
= 21 u - 15 u
= 6 u

6 u = 210

1 u = 210 ÷ 6 = 35

Amount that Julie spent
= 10 u
= 10 x 35
= $350 

Answer(s): (a) 10 : 15 : 21; (b) $350