Question

Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Find the number of months after which they will have the same number of CDs. show your work

Answer 1

30:18,
31:23
32:28
33:33
It will be three months before they have the same amount of CDs

Answer 2

3 months.

Explanation:

Let x represent the number of months.

We have been given that Tom has a collection of 30 CDs and he is adding 1 CD a month to his collection.

So number of CDs in Tom's collection after x months would be:
`30+x`.

We are also told that Nita has a collection of 18 CDs. Nita is adding 5 CDs a month to her collection. So number of CDs in Nita's collection after x months would be:
`18+5x`.

To solve for number of months, when both will have same number of CDs, we will equate both expressions as:

`18+5x=30+x`

`18+5x-x=30+x-x`

`18+4x=30`

`18-18+4x=30-18`

`4x=12`

`(4x)/(4)=(12)/(4)`

`x=3`

Therefore, after 3 months they will have the same number of CDs.