Three women, Irene, Fanny and Cathy went on a shopping spree. 70% of Irene's spending was equal to ¹₆ of Fanny's spending. Cathy's spending was  60% less than Fanny's. If Fanny spent $5355 less, she would spend the same amount of money as Cathy.

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

Irene	Fanny	Cathy
5x5	21x5
	5x21	2x21
25 u	105 u	42 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Irene's spending is equal to ¹₆ of Fanny's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Irene's spending = 16 of Fanny's spending
710 of Irene's spending =1x76x7 of Fanny's spending
710 of Irene's spending = 742 of Fanny's spending

Irene : Fanny
10 : 42
5 : 21

Cathy's spending in percent when compared to Fanny's
= 100% - 60%
= 40%

Fanny : Cathy
100 : 40
5 : 2

Fanny's spending is the repeated identity.  Make Fanny's spending the same.  LCM of 21 and 5 is 105.

Irene : Fanny : Cathy
25 : 105 : 42

(b)

	Irene	Fanny	Cathy
Before	25 u	105 u	42 u
Change		- 63 u
After	25 u	42 u	42 u

Additional amount that Fanny would have to spend less to be the same as Cathy
= 105 u - 42 u
= 63 u

63 u = 5355

1 u = 5355 ÷ 63 = 85

Amount that Cathy spent
= 42 u
= 42 x 85
= $3570 

Answer(s): (a) 25 : 105 : 42; (b) $3570