Three women, Jean, Barbara and Elyse went on a shopping spree. 70% of Jean's spending was equal to ¹₅ of Barbara's spending. Elyse's spending was  50% more than Barbara's. If Barbara spent another $700, she would spend the same amount of money as Elyse.

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

Jean	Barbara	Elyse
2x2	7x2
	2x7	3x7
4 u	14 u	21 u

(a)
70%= ⁷⁰₁₀₀ = ⁷₁₀
⁷₁₀ of Jean's spending is equal to ¹₅ of Barbara's spending. Make the numerators the same.  LCM of 7 and 1 is 7.

710 of Jean's spending = 15 of Barbara's spending
710 of Jean's spending =1x75x7 of Barbara's spending
710 of Jean's spending = 735 of Barbara's spending

Jean : Barbara
10 : 35
2 : 7

Elyse's spending in percent when compared to Barbara's
= 100% + 50%
= 150%

Barbara : Elyse
100 : 150
2 : 3

Barbara's spending is the repeated identity.  Make Barbara's spending the same.  LCM of 7 and 2 is 14.

Jean : Barbara : Elyse
4 : 14 : 21

(b)

	Jean	Barbara	Elyse
Before	4 u	14 u	21 u
Change		+ 7 u
After	4 u	21 u	21 u

Additional amount that Barbara would have to spend to be the same as Elyse
= 21 u - 14 u
= 7 u

7 u = 700

1 u = 700 ÷ 7 = 100

Amount that Jean spent
= 4 u
= 4 x 100
= $400 

Answer(s): (a) 4 : 14 : 21; (b) $400