Three women, Esther, Vanessa and Jaslyn went on a shopping spree. 70% of Esther's spending was equal to ¹₂ of Vanessa's spending. Jaslyn's spending was  25% less than Vanessa's. If Vanessa spent $476 less, she would spend the same amount of money as Jaslyn.

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

Esther	Vanessa	Jaslyn
5x4	7x4
	4x7	3x7
20 u	28 u	21 u

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

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

Esther : Vanessa
10 : 14
5 : 7

Jaslyn's spending in percent when compared to Vanessa's
= 100% - 25%
= 75%

Vanessa : Jaslyn
100 : 75
4 : 3

Vanessa's spending is the repeated identity.  Make Vanessa's spending the same.  LCM of 7 and 4 is 28.

Esther : Vanessa : Jaslyn
20 : 28 : 21

(b)

	Esther	Vanessa	Jaslyn
Before	20 u	28 u	21 u
Change		- 7 u
After	20 u	21 u	21 u

Additional amount that Vanessa would have to spend less to be the same as Jaslyn
= 28 u - 21 u
= 7 u

7 u = 476

1 u = 476 ÷ 7 = 68

Amount that Jaslyn spent
= 21 u
= 21 x 68
= $1428 

Answer(s): (a) 20 : 28 : 21; (b) $1428