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
`\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=(114)/(9.5)`

`d=12`

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