Question

skylar repairs microwaves her revenue equals R(h)=80+30h for every h hour she spends repairing microwaves. Her overhead costs C(h)=10h2-20, After how many hours does she break even

Answer 1

To break even, means her revenue and overhead are equal, i.e. she isn't making any money but isn't losing any either. We can write an equation to represent this situation:


`R(h)=C(h)`

`80+30h=10h^(2)-20`

And then solve for h:

`10h^(2)-30h-100=0`
We can solve with the quadratic formula, or more easily, by factoring:

`10(h-5)(h+2)=0`
So either

`h-5=0` OR
`h+2=0`

`h=5`
`h=-2`

Since a negative number of hours makes no sense: h=5.

She will break even after 5 hours.