Penelope, Jade and Gwen had a sum of money. The amount of money Penelope had was ³₄ of the amount of money Jade had. The ratio of the amount of money Jade had to the total amount of money Gwen and Jade had was 2: 5. After Gwen gave $50 to Jade, she had as much money as Jade. How much more money did Gwen have than Penelope in the end?

Penelope	Jade	Gwen
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

The amount that Jade had is the repeated identity. Make the amount that Jade had the same.  LCM of 4 and 2 is 4.

	Penelope	Jade	Gwen
Before	3 u	4 u	6 u
Change	No change	+ 50	- 50
After	3 u	4 u + 50	6 u - 50

The amount that Gwen and Jade had in the end is the same.

6 u - 50 = 4 u + 50
6 u - 4 u = 50 + 50 
2 u = 100

1 u = 100 ÷ 2 = 50

Amount that Gwen had more than Penelope in the end
= 6 u - 50 - 3 u
= 3 u - 50
= 3 x 50 - 50
= 150 - 50
= $100

Answer(s): $100