Answer:
3 months.
Step-by-step 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:
\(18+5x=30+x\)
\(18+5x-x=30+x-x\)
\(18+4x=30\)
\(18-18+4x=30-18\)
\(4x=12\)
\(\frac{4x}{4}=\frac{12}{4}\)
\(x=3\)
Therefore, after 3 months they will have the same number of CDs.
