Question

Internet rates for two companies are shown in the table. After how many months of service is the total cost thesame no matter which company is used? What is this total cost?Intemet Service ProviderChargesTyson's Ethernet $100 activation fee plus $20 per monthDarriana's DSL$30 per month

Answer 1

We need to find in which month we have that the total cost is the same, so we are going to do the equations of cost of the two companies

For the Tyson's Ethernet we have that the equation is

`f(m)=20\cdot m+100`

with m the month. And for the Darriana's DSL the equation is

`g(m)=30\cdot m`

We need to equalize the equations, so we have

`\begin{gathered} 30m=20m+100 \\ 30m-20m=20m+100-20m \\ 10m=100 \\ m=(100)/(10)=10 \end{gathered}`

Now to see the cost we replace in the two equations( wiith this we also verify), we have that

`\begin{gathered} f(10)=20\cdot10+100=200+100=300 \\ g(10)=30\cdot10=300 \end{gathered}`

The answer is: after 10 months the total cost is the same, and this cost is $300.