Zoe, Lucy and Joelle had a sum of money. The amount of money Zoe had was ⁴₅ of the amount of money Lucy had. The ratio of the amount of money Lucy had to the total amount of money Joelle and Lucy had was 2: 5. After Joelle gave $80 to Lucy, she had as much money as Lucy. How much more money did Joelle have than Zoe in the end?

Zoe	Lucy	Joelle
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

The amount that Lucy had is the repeated identity. Make the amount that Lucy had the same.  LCM of 5 and 2 is 10.

	Zoe	Lucy	Joelle
Before	8 u	10 u	15 u
Change	No change	+ 80	- 80
After	8 u	10 u + 80	15 u - 80

The amount that Joelle and Lucy had in the end is the same.

15 u - 80 = 10 u + 80
15 u - 10 u = 80 + 80 
5 u = 160

1 u = 160 ÷ 5 = 32

Amount that Joelle had more than Zoe in the end
= 15 u - 80 - 8 u
= 7 u - 80
= 7 x 32 - 80
= 224 - 80
= $144

Answer(s): $144