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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.

Respuesta :

twvogels

For a non-resident:

[tex]C_{nr}=8d+2.5d=10.5d[/tex]

For a resident:

[tex]C_{r}=114+1d[/tex]

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

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

[tex]C_{nr}=C_{r}[/tex]

[tex]10.5d=114+1d[/tex]

And solve for d:

[tex]10.5d-1d=114+1d-1d[/tex]

[tex]9.5d=114[/tex]

[tex]d=\frac{114}{9.5}[/tex]

[tex]d=12[/tex]

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