Three women, Vanessa, Lynn and Jean went on a shopping spree. 70% of Vanessa's spending was equal to ¹₂ of Lynn's spending. Jean's spending was  40% less than Lynn's. If Lynn spent $784 less, she would spend the same amount of money as Jean.

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

Vanessa	Lynn	Jean
5x5	7x5
	5x7	3x7
25 u	35 u	21 u

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

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

Vanessa : Lynn
10 : 14
5 : 7

Jean's spending in percent when compared to Lynn's
= 100% - 40%
= 60%

Lynn : Jean
100 : 60
5 : 3

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

Vanessa : Lynn : Jean
25 : 35 : 21

(b)

	Vanessa	Lynn	Jean
Before	25 u	35 u	21 u
Change		- 14 u
After	25 u	21 u	21 u

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

14 u = 784

1 u = 784 ÷ 14 = 56

Amount that Jean spent
= 21 u
= 21 x 56
= $1176 

Answer(s): (a) 25 : 35 : 21; (b) $1176