Three women, Gillian, Marion and Gem went on a shopping spree. 90% of Gillian's spending was equal to ¹₂ of Marion's spending. Gem's spending was  80% less than Marion's. If Marion spent $1800 less, she would spend the same amount of money as Gem.

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

Gillian	Marion	Gem
5x5	9x5
	5x9	1x9
25 u	45 u	9 u

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

910 of Gillian's spending = 12 of Marion's spending
910 of Gillian's spending =1x92x9 of Marion's spending
910 of Gillian's spending = 918 of Marion's spending

Gillian : Marion
10 : 18
5 : 9

Gem's spending in percent when compared to Marion's
= 100% - 80%
= 20%

Marion : Gem
100 : 20
5 : 1

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

Gillian : Marion : Gem
25 : 45 : 9

(b)

	Gillian	Marion	Gem
Before	25 u	45 u	9 u
Change		- 36 u
After	25 u	9 u	9 u

Additional amount that Marion would have to spend less to be the same as Gem
= 45 u - 9 u
= 36 u

36 u = 1800

1 u = 1800 ÷ 36 = 50

Amount that Gem spent
= 9 u
= 9 x 50
= $450 

Answer(s): (a) 25 : 45 : 9; (b) $450