Three women, Gem, Shannon and Tiffany went on a shopping spree. 90% of Gem's spending was equal to ¹₅ of Shannon's spending. Tiffany's spending was  80% less than Shannon's. If Shannon spent $2988 less, she would spend the same amount of money as Tiffany.

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

Gem	Shannon	Tiffany
2x5	9x5
	5x9	1x9
10 u	45 u	9 u

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

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

Gem : Shannon
10 : 45
2 : 9

Tiffany's spending in percent when compared to Shannon's
= 100% - 80%
= 20%

Shannon : Tiffany
100 : 20
5 : 1

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

Gem : Shannon : Tiffany
10 : 45 : 9

(b)

	Gem	Shannon	Tiffany
Before	10 u	45 u	9 u
Change		- 36 u
After	10 u	9 u	9 u

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

36 u = 2988

1 u = 2988 ÷ 36 = 83

Amount that Tiffany spent
= 9 u
= 9 x 83
= $747 

Answer(s): (a) 10 : 45 : 9; (b) $747