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

Xuan	Lynn	Hazel
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

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

	Xuan	Lynn	Hazel
Before	12 u	15 u	20 u
Change	No change	+ 45	- 45
After	12 u	15 u + 45	20 u - 45

The amount that Hazel and Lynn had in the end is the same.

20 u - 45 = 15 u + 45
20 u - 15 u = 45 + 45 
5 u = 90

1 u = 90 ÷ 5 = 18

Amount that Hazel had more than Xuan in the end
= 20 u - 45 - 12 u
= 8 u - 45
= 8 x 18 - 45
= 144 - 45
= $99

Answer(s): $99