Three women, Vanessa, Kathy and Emily went on a shopping spree. 70% of Vanessa's spending was equal to ¹₂ of Kathy's spending. Emily's spending was  40% less than Kathy's. If Kathy spent $1596 less, she would spend the same amount of money as Emily.

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

Vanessa	Kathy	Emily
5x5	7x5
	5x7	3x7
25 u	35 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Vanessa's spending is equal to ¹₂ of Kathy's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Vanessa's spending = 12 of Kathy's spending
710 of Vanessa's spending =1x72x7 of Kathy's spending
710 of Vanessa's spending = 714 of Kathy's spending

Vanessa : Kathy
10 : 14
5 : 7

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

Kathy : Emily
100 : 60
5 : 3

Kathy's spending is the repeated identity.  Make Kathy's spending the same.  LCM of 7 and 5 is 35.

Vanessa : Kathy : Emily
25 : 35 : 21

(b)

	Vanessa	Kathy	Emily
Before	25 u	35 u	21 u
Change		- 14 u
After	25 u	21 u	21 u

Additional amount that Kathy would have to spend less to be the same as Emily
= 35 u - 21 u
= 14 u

14 u = 1596

1 u = 1596 ÷ 14 = 114

Amount that Emily spent
= 21 u
= 21 x 114
= $2394 

Answer(s): (a) 25 : 35 : 21; (b) $2394