Xandra, Hilda and Nora had a sum of money. The amount of money Xandra had was ⁴₅ of the amount of money Hilda had. The ratio of the amount of money Hilda had to the total amount of money Nora and Hilda had was 3: 8. After Nora gave $40 to Hilda, she had as much money as Hilda. How much more money did Nora have than Xandra in the end?

Xandra	Hilda	Nora
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
12 u	15 u	25 u

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

	Xandra	Hilda	Nora
Before	12 u	15 u	25 u
Change	No change	+ 40	- 40
After	12 u	15 u + 40	25 u - 40

The amount that Nora and Hilda had in the end is the same.

25 u - 40 = 15 u + 40
25 u - 15 u = 40 + 40 
10 u = 80

1 u = 80 ÷ 10 = 8

Amount that Nora had more than Xandra in the end
= 25 u - 40 - 12 u
= 13 u - 40
= 13 x 8 - 40
= 104 - 40
= $64

Answer(s): $64