Three women, Jen, Elyse and Kathy went on a shopping spree. 70% of Jen's spending was equal to ¹₆ of Elyse's spending. Kathy's spending was  40% less than Elyse's. If Elyse spent $1932 less, she would spend the same amount of money as Kathy.

1. Find the ratio of Jen's spending to Elyse's to Kathy's.
2. How much did Kathy spend?

Jen	Elyse	Kathy
5x5	21x5
	5x21	3x21
25 u	105 u	63 u

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

710 of Jen's spending = 16 of Elyse's spending
710 of Jen's spending =1x76x7 of Elyse's spending
710 of Jen's spending = 742 of Elyse's spending

Jen : Elyse
10 : 42
5 : 21

Kathy's spending in percent when compared to Elyse's
= 100% - 40%
= 60%

Elyse : Kathy
100 : 60
5 : 3

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

Jen : Elyse : Kathy
25 : 105 : 63

(b)

	Jen	Elyse	Kathy
Before	25 u	105 u	63 u
Change		- 42 u
After	25 u	63 u	63 u

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

42 u = 1932

1 u = 1932 ÷ 42 = 46

Amount that Kathy spent
= 63 u
= 63 x 46
= $2898 

Answer(s): (a) 25 : 105 : 63; (b) $2898