Three women, Cathy, Tiffany and Gabby went on a shopping spree. 90% of Cathy's spending was equal to ¹₂ of Tiffany's spending. Gabby's spending was  70% less than Tiffany's. If Tiffany spent $5355 less, she would spend the same amount of money as Gabby.

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

Cathy	Tiffany	Gabby
5x10	9x10
	10x9	3x9
50 u	90 u	27 u

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

910 of Cathy's spending = 12 of Tiffany's spending
910 of Cathy's spending =1x92x9 of Tiffany's spending
910 of Cathy's spending = 918 of Tiffany's spending

Cathy : Tiffany
10 : 18
5 : 9

Gabby's spending in percent when compared to Tiffany's
= 100% - 70%
= 30%

Tiffany : Gabby
100 : 30
10 : 3

Tiffany's spending is the repeated identity.  Make Tiffany's spending the same.  LCM of 9 and 10 is 90.

Cathy : Tiffany : Gabby
50 : 90 : 27

(b)

	Cathy	Tiffany	Gabby
Before	50 u	90 u	27 u
Change		- 63 u
After	50 u	27 u	27 u

Additional amount that Tiffany would have to spend less to be the same as Gabby
= 90 u - 27 u
= 63 u

63 u = 5355

1 u = 5355 ÷ 63 = 85

Amount that Gabby spent
= 27 u
= 27 x 85
= $2295 

Answer(s): (a) 50 : 90 : 27; (b) $2295