Min had $990 less than Ken. Min spent ¹₆ of her money and Ken spent ²₃ of his money. In the end, Ken and Min had the same amount of money left. Find the amount of money Ken had at first.

	Min	Ken	Difference
Before	6x1 = 6 u	3x5 = 15 u	9 u
Change	- 1x1 = - 1 u	- 2x5 = - 10 u
After	5x1 = 5 u	1x5 = 5 u

Fraction of Min's money left
= 1 - ¹₆
= ⁵₆

Fraction of Ken's money left
= 1 - ²₃
= ¹₃

Ken and Min had the same amount of money in the end. Make the numerators the same. LCM of 5 and 1 is 5.

⁵₆ of Min's money = ¹₃ of Ken's money
⁵₆ of Min's money = ⁵₁₅ of Ken's money

Amount that Min had at first = 6 u
Amount that Ken had at first = 15 u

Amount that Min had less than Ken had at first
= 15 u - 6 u
= 9 u

9 u = 990

1 u = 990 ÷ 9 = 110

Amount that Ken had at first
= 15 u
= 15 x 110
= $1650

Answer(s): $1650