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

(1 point)
Responses

1 month
1 month

3 months
3 months

2 months
2 months

33 months

Answer 1

Let x represent the number of months it takes for Tom and Nita to have the same number of CDs.

After x months, Tom will have 30 + x CDs and Nita will have 18 + 5x CDs.

Setting the two expressions equal to each other, we have:

30 + x = 18 + 5x

Subtracting 18 from both sides, we have:

12 + x = 5x

Subtracting x from both sides, we have:

12 = 4x

Dividing both sides by 4, we have:

x = 3

Therefore, it will take Tom and Nita 3 months to have the same number of CDs. Answer: 3 months.