Jane, Gillian and Hilda had a sum of money. The amount of money Jane had was ⁴₅ of the amount of money Gillian had. The ratio of the amount of money Gillian had to the total amount of money Hilda and Gillian had was 3: 7. After Hilda gave $100 to Gillian, she had as much money as Gillian. How much more money did Hilda have than Jane in the end?

Jane	Gillian	Hilda
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

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

	Jane	Gillian	Hilda
Before	12 u	15 u	20 u
Change	No change	+ 100	- 100
After	12 u	15 u + 100	20 u - 100

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

20 u - 100 = 15 u + 100
20 u - 15 u = 100 + 100 
5 u = 200

1 u = 200 ÷ 5 = 40

Amount that Hilda had more than Jane in the end
= 20 u - 100 - 12 u
= 8 u - 100
= 8 x 40 - 100
= 320 - 100
= $220

Answer(s): $220