Jean, Jen and Shannon had a sum of money. The amount of money Jean had was ²₅ of the amount of money Jen had. The ratio of the amount of money Jen had to the total amount of money Shannon and Jen had was 3: 7. After Shannon gave $75 to Jen, she had as much money as Jen. How much more money did Shannon have than Jean in the end?

Jean	Jen	Shannon
2x3 = 6 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
6 u	15 u	20 u

The amount that Jen had is the repeated identity. Make the amount that Jen had the same.  LCM of 5 and 3 is 15.

	Jean	Jen	Shannon
Before	6 u	15 u	20 u
Change	No change	+ 75	- 75
After	6 u	15 u + 75	20 u - 75

The amount that Shannon and Jen had in the end is the same.

20 u - 75 = 15 u + 75
20 u - 15 u = 75 + 75 
5 u = 150

1 u = 150 ÷ 5 = 30

Amount that Shannon had more than Jean in the end
= 20 u - 75 - 6 u
= 14 u - 75
= 14 x 30 - 75
= 420 - 75
= $345

Answer(s): $345