Fiona, Rachel and Betty had a sum of money. The amount of money Fiona had was ⁴₅ of the amount of money Rachel had. The ratio of the amount of money Rachel had to the total amount of money Betty and Rachel had was 4: 9. After Betty gave $40 to Rachel, she had as much money as Rachel. How much more money did Betty have than Fiona in the end?

Fiona	Rachel	Betty
4x4 = 16 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
16 u	20 u	25 u

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

	Fiona	Rachel	Betty
Before	16 u	20 u	25 u
Change	No change	+ 40	- 40
After	16 u	20 u + 40	25 u - 40

The amount that Betty and Rachel had in the end is the same.

25 u - 40 = 20 u + 40
25 u - 20 u = 40 + 40 
5 u = 80

1 u = 80 ÷ 5 = 16

Amount that Betty had more than Fiona in the end
= 25 u - 40 - 16 u
= 9 u - 40
= 9 x 16 - 40
= 144 - 40
= $104

Answer(s): $104