Question

a long distance telephone call using down east calling costs 25 cents for the first minute and 16 cents for each additional minute. The same call, placed on long call system, costs 20 cents for the first minute and 18 cents for each additional minute. For what lenght phone calls is down east calling more expensive?

Answer 1

the answer was less than 3 and 1/2 minutes, but i got 2 and 1/2.what did i do wrong?

Answer 2

We have:
\[
P_E=.25+.16x\\
P_L=.20+.18x
\]Where x is the number of *additional* minutes. Hence:
\[
P_E<P_L
\]Becomes:
\[
\begin{align}
.25+.16x&<.20+.18x\iff\\
.05&<.02x\iff\\
2.5&<x
\end{align}
\]Hence, the number of *additional* minutes is 2.5. But our first minutes is not counted, so we have that \(2.5+1=3.5\), which is our final answer.

Answer 3

oh i see thanks