Three women, Gabby, Cathy and Gillian went on a shopping spree. 90% of Gabby's spending was equal to ¹₅ of Cathy's spending. Gillian's spending was  70% less than Cathy's. If Cathy spent $2835 less, she would spend the same amount of money as Gillian.

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

Gabby	Cathy	Gillian
2x10	9x10
	10x9	3x9
20 u	90 u	27 u

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

910 of Gabby's spending = 15 of Cathy's spending
910 of Gabby's spending =1x95x9 of Cathy's spending
910 of Gabby's spending = 945 of Cathy's spending

Gabby : Cathy
10 : 45
2 : 9

Gillian's spending in percent when compared to Cathy's
= 100% - 70%
= 30%

Cathy : Gillian
100 : 30
10 : 3

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

Gabby : Cathy : Gillian
20 : 90 : 27

(b)

	Gabby	Cathy	Gillian
Before	20 u	90 u	27 u
Change		- 63 u
After	20 u	27 u	27 u

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

63 u = 2835

1 u = 2835 ÷ 63 = 45

Amount that Gillian spent
= 27 u
= 27 x 45
= $1215 

Answer(s): (a) 20 : 90 : 27; (b) $1215