Diana, Kimberly and Lynn had a sum of money. The amount of money Diana had was ⁴₅ of the amount of money Kimberly had. The ratio of the amount of money Kimberly had to the total amount of money Lynn and Kimberly had was 2: 5. After Lynn gave $85 to Kimberly, she had as much money as Kimberly. How much more money did Lynn have than Diana in the end?

Diana	Kimberly	Lynn
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

The amount that Kimberly had is the repeated identity. Make the amount that Kimberly had the same.  LCM of 5 and 2 is 10.

	Diana	Kimberly	Lynn
Before	8 u	10 u	15 u
Change	No change	+ 85	- 85
After	8 u	10 u + 85	15 u - 85

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

15 u - 85 = 10 u + 85
15 u - 10 u = 85 + 85 
5 u = 170

1 u = 170 ÷ 5 = 34

Amount that Lynn had more than Diana in the end
= 15 u - 85 - 8 u
= 7 u - 85
= 7 x 34 - 85
= 238 - 85
= $153

Answer(s): $153