Tom has a collection of 30 CDs, and Nita has a collection of 18 CDs. Tom is adding 1 CD per month to his collection, while Nita is adding 5 CDs per month to her collection. After how many months will Tom and Nita have the same number of CDs? Write and solve a system of equations.
Let $m$ be the number of months since Nita started adding CDs to her collection. Then the number of CDs that Nita has is $18 + 5m,$ and the number of CDs that Tom has is $30 + m.$ If the number of CDs is the same, then
\[18 + 5m = 30 + m.\]Solving, we find $m = \boxed{2}.$