<div>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.</div>

Question

<div>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.</div>

Answer 1

Let's say after $m$ months, Tom will have $30+m$ CDs, and Nita will have $18+5m$ CDs. We want to find when the two quantities are equal. Thus, we set up the equation \begin{align*}

30+m&=18+5m \\
\Rightarrow\qquad 30&=18+4m \\
\Rightarrow\qquad 12&=4m \\
\Rightarrow\qquad \boxed{3}&=m
\end{align*}So after 3 months, the number of CDs that Tom and Nita have will be the same.