Three women, Joelle, Gem and Kylie went on a shopping spree. 70% of Joelle's spending was equal to ¹₂ of Gem's spending. Kylie's spending was  50% more than Gem's. If Gem spent another $210, she would spend the same amount of money as Kylie.

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

Joelle	Gem	Kylie
5x2	7x2
	2x7	3x7
10 u	14 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Joelle's spending is equal to ¹₂ of Gem's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Joelle's spending = 12 of Gem's spending
710 of Joelle's spending =1x72x7 of Gem's spending
710 of Joelle's spending = 714 of Gem's spending

Joelle : Gem
10 : 14
5 : 7

Kylie's spending in percent when compared to Gem's
= 100% + 50%
= 150%

Gem : Kylie
100 : 150
2 : 3

Gem's spending is the repeated identity.  Make Gem's spending the same.  LCM of 7 and 2 is 14.

Joelle : Gem : Kylie
10 : 14 : 21

(b)

	Joelle	Gem	Kylie
Before	10 u	14 u	21 u
Change		+ 7 u
After	10 u	21 u	21 u

Additional amount that Gem would have to spend to be the same as Kylie
= 21 u - 14 u
= 7 u

7 u = 210

1 u = 210 ÷ 7 = 30

Amount that Joelle spent
= 10 u
= 10 x 30
= $300 

Answer(s): (a) 10 : 14 : 21; (b) $300