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

Roshel	Olivia	Xuan
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

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

	Roshel	Olivia	Xuan
Before	12 u	15 u	20 u
Change	No change	+ 100	- 100
After	12 u	15 u + 100	20 u - 100

The amount that Xuan and Olivia 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 Xuan had more than Roshel in the end
= 20 u - 100 - 12 u
= 8 u - 100
= 8 x 40 - 100
= 320 - 100
= $220

Answer(s): $220