Gem, Jaslyn and Hazel had a sum of money. The amount of money Gem had was ⁴₅ of the amount of money Jaslyn had. The ratio of the amount of money Jaslyn had to the total amount of money Hazel and Jaslyn had was 4: 9. After Hazel gave $75 to Jaslyn, she had as much money as Jaslyn. How much more money did Hazel have than Gem in the end?

Gem	Jaslyn	Hazel
4x4 = 16 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
16 u	20 u	25 u

The amount that Jaslyn had is the repeated identity. Make the amount that Jaslyn had the same.  LCM of 5 and 4 is 20.

	Gem	Jaslyn	Hazel
Before	16 u	20 u	25 u
Change	No change	+ 75	- 75
After	16 u	20 u + 75	25 u - 75

The amount that Hazel and Jaslyn had in the end is the same.

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

1 u = 150 ÷ 5 = 30

Amount that Hazel had more than Gem in the end
= 25 u - 75 - 16 u
= 9 u - 75
= 9 x 30 - 75
= 270 - 75
= $195

Answer(s): $195