Three women, Dana, Jade and Gem went on a shopping spree. 90% of Dana's spending was equal to ¹₂ of Jade's spending. Gem's spending was  40% more than Jade's. If Jade spent another $1872, she would spend the same amount of money as Gem.

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

Dana	Jade	Gem
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

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

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

Dana : Jade
10 : 18
5 : 9

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

Jade : Gem
100 : 140
5 : 7

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

Dana : Jade : Gem
25 : 45 : 63

(b)

	Dana	Jade	Gem
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Jade would have to spend to be the same as Gem
= 63 u - 45 u
= 18 u

18 u = 1872

1 u = 1872 ÷ 18 = 104

Amount that Dana spent
= 25 u
= 25 x 104
= $2600 

Answer(s): (a) 25 : 45 : 63; (b) $2600