Question

eric has a summer lawn mowing buisness. based on experience eric knows that p= -3x^2 + 150x -1200 models his profit, p, in dollars, where x is the amount he charges per lawn. how much does he need to charge if he wants to break even? show your work

Answer 1

Eric can either charge $10 or $40 in order to break even.

Explanation:

Eric has a summer lawn mowing business and the equation:

`p=-3x^2+150x-1200`

Models his total profit p by charging x dollars per lawn.

We want to determine what price Eric needs to charge in order to break even.

The price Eric charges to break even means that his total profit will be zero. Hence, we can let p = 0 and solve for x. Thu:

`0=-3x^2+150x-1200`

We can divide both sides by -3:

`0=x^2-50x+400`

Factor:

`0=(x-10)(x-40)`

Zero Product Property:

`x-10=0\text{ or } x-40=0`

Solve for each case. Hence:

`x=10\text{ or } x=40`

Therefore, Eric can either charge $10 or $40 in order to break even.