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.

Question

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.

Responses:

1 month
3 months
2 months
33 months

Answer 1

Let's assume that after "m" months, Tom and Nita will have the same number of CDs.

After "m" months, Tom will have 30 + m CDs.
After "m" months, Nita will have 18 + 5m CDs.

So we can set up the following system of equations:
30 + m = 18 + 5m

Subtracting m from both sides:
30 = 18 + 4m

Subtracting 18 from both sides:
12 = 4m

Dividing both sides by 4:
3 = m

Therefore, after 3 months, Tom and Nita will have the same number of CDs.