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
[tex]f(m)=20\cdot m+100[/tex]with m the month. And for the Darriana's DSL the equation is
[tex]g(m)=30\cdot m[/tex]We need to equalize the equations, so we have
[tex]\begin{gathered} 30m=20m+100 \\ 30m-20m=20m+100-20m \\ 10m=100 \\ m=\frac{100}{10}=10 \end{gathered}[/tex]Now to see the cost we replace in the two equations( wiith this we also verify), we have that
[tex]\begin{gathered} f(10)=20\cdot10+100=200+100=300 \\ g(10)=30\cdot10=300 \end{gathered}[/tex]The answer is: after 10 months the total cost is the same, and this cost is $300.
