Three women, Fanny, Gem and Ivory went on a shopping spree. 90% of Fanny's spending was equal to ¹₅ of Gem's spending. Ivory's spending was  80% less than Gem's. If Gem spent $4068 less, she would spend the same amount of money as Ivory.

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

Fanny	Gem	Ivory
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Fanny's spending is equal to ¹₅ of Gem's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Fanny's spending = 15 of Gem's spending
910 of Fanny's spending =1x95x9 of Gem's spending
910 of Fanny's spending = 945 of Gem's spending

Fanny : Gem
10 : 45
2 : 9

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

Gem : Ivory
100 : 20
5 : 1

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

Fanny : Gem : Ivory
10 : 45 : 9

(b)

	Fanny	Gem	Ivory
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

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

36 u = 4068

1 u = 4068 ÷ 36 = 113

Amount that Ivory spent
= 9 u
= 9 x 113
= $1017 

Answer(s): (a) 10 : 45 : 9; (b) $1017