Lynn, Yen and Nicole had a sum of money. The amount of money Lynn had was ⁴₅ of the amount of money Yen had. The ratio of the amount of money Yen had to the total amount of money Nicole and Yen had was 2: 5. After Nicole gave $90 to Yen, she had as much money as Yen. How much more money did Nicole have than Lynn in the end?

Lynn	Yen	Nicole
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

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

	Lynn	Yen	Nicole
Before	8 u	10 u	15 u
Change	No change	+ 90	- 90
After	8 u	10 u + 90	15 u - 90

The amount that Nicole and Yen had in the end is the same.

15 u - 90 = 10 u + 90
15 u - 10 u = 90 + 90 
5 u = 180

1 u = 180 ÷ 5 = 36

Amount that Nicole had more than Lynn in the end
= 15 u - 90 - 8 u
= 7 u - 90
= 7 x 36 - 90
= 252 - 90
= $162

Answer(s): $162