Question

A public beach in Florida charges non residents $8 per day for a fishing license and $2.50 per day for live bait. Florida residents pay an anual fee of $114 plus $1 per day for live bait. How many days must both a resident and a non resident use the beach in one year so that both pay the same amount? Show all work.

Answer 1

For a non-resident:

$C_{nr}=8d+2.5d=10.5d$

For a resident:

$C_{r}=114+1d$

We want to know the number of days $d$ such that the two costs are equal ie $\{d|C_{nr}(d)=C_{r}(d)\}$

To do this set the two costs equal to each other:

$C_{nr}=C_{r}$

$10.5d=114+1d$

And solve for d:

$10.5d-1d=114+1d-1d$

$9.5d=114$

$d=\frac{114}{9.5}$

$d=12$

The costs will be equal when a resident and a non-resident each use the beach for 12 days.