Three women, Gem, Dana and Jade went on a shopping spree. 90% of Gem's spending was equal to ¹₂ of Dana's spending. Jade's spending was  60% less than Dana's. If Dana spent $2349 less, she would spend the same amount of money as Jade.

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

Gem	Dana	Jade
5x5	9x5
	5x9	2x9
25 u	45 u	18 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Gem's spending is equal to ¹₂ of Dana's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Gem's spending = 12 of Dana's spending
910 of Gem's spending =1x92x9 of Dana's spending
910 of Gem's spending = 918 of Dana's spending

Gem : Dana
10 : 18
5 : 9

Jade's spending in percent when compared to Dana's
= 100% - 60%
= 40%

Dana : Jade
100 : 40
5 : 2

Dana's spending is the repeated identity.  Make Dana's spending the same.  LCM of 9 and 5 is 45.

Gem : Dana : Jade
25 : 45 : 18

(b)

	Gem	Dana	Jade
Before	25 u	45 u	18 u
Change		- 27 u
After	25 u	18 u	18 u

Additional amount that Dana would have to spend less to be the same as Jade
= 45 u - 18 u
= 27 u

27 u = 2349

1 u = 2349 ÷ 27 = 87

Amount that Jade spent
= 18 u
= 18 x 87
= $1566 

Answer(s): (a) 25 : 45 : 18; (b) $1566