Question

9. You are considering getting a new cell phone with texting privileges. Cell PhoneAmerica charges $40 a month and $0.39 per text message. Call on me charges $30 amonth and $0.49 per text message. After how many text messages would bothcompanies charge the same amount?

Answer 1

Let N be the number of text messages sent.

The charge for N messages in one company will be:

`40+0.39N`

While on the other company, it will be:

`30+0.49N`

If after N messages, the charge is the same in both companies, then:

`40+0.39N=30+0.49N`

Solve this equation for N:

`\begin{gathered} 0.49N-0.39N=40-30 \\ \Rightarrow0.1N=10 \\ \Rightarrow N=100 \end{gathered}`

Therefore, both companies will charge the same at 100 messages sent.