Three women, Raeann, Gem and Jaslyn went on a shopping spree. 70% of Raeann's spending was equal to ¹₅ of Gem's spending. Jaslyn's spending was  40% more than Gem's. If Gem spent another $1414, she would spend the same amount of money as Jaslyn.

1. Find the ratio of Raeann's spending to Gem's to Jaslyn's.
2. How much did Raeann spend?

Raeann	Gem	Jaslyn
2x5	7x5
	5x7	7x7
10 u	35 u	49 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Raeann's spending is equal to ¹₅ of Gem's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Raeann's spending = 15 of Gem's spending
710 of Raeann's spending =1x75x7 of Gem's spending
710 of Raeann's spending = 735 of Gem's spending

Raeann : Gem
10 : 35
2 : 7

Jaslyn's spending in percent when compared to Gem's
= 100% + 40%
= 140%

Gem : Jaslyn
100 : 140
5 : 7

Gem's spending is the repeated identity.  Make Gem's spending the same.  LCM of 7 and 5 is 35.

Raeann : Gem : Jaslyn
10 : 35 : 49

(b)

	Raeann	Gem	Jaslyn
Before	10 u	35 u	49 u
Change		+ 14 u
After	10 u	49 u	49 u

Additional amount that Gem would have to spend to be the same as Jaslyn
= 49 u - 35 u
= 14 u

14 u = 1414

1 u = 1414 ÷ 14 = 101

Amount that Raeann spent
= 10 u
= 10 x 101
= $1010 

Answer(s): (a) 10 : 35 : 49; (b) $1010