How many hours does she break even?

revenue  =  R(h)  =  20 + 30h

 

cost  =  C(h)  =  10h² - 80

 

In how many hours does she break even?  This means...

 

How many hours does it take for revenue to equal cost?

 

What is the value of  h  when  revenue  =  cost   ?

 

What is the value of  h  when   20 + 30h   =   10h² - 80   ?

 

20 + 30h   =   10h² - 80      We want to solve this equation for  h .

                                           Subtract  30h  from both sides.

20   =   10h² - 30h - 80

                                           Subtract  20  from both sides.

0   =   10h² - 30h - 100

                                           Divide through by  10 .

0   =   h² - 3h - 10

                                           Factor the right side of the equation.

0   =   (h - 5)(h + 2)

                                           Set each factor equal to zero.

h - 5  =  0    or    h + 2 = 0

h  =  5         or    h  =  -2

 

Since  h  is the number of hours it takes to break even, we only want to include the positive solution.

 

h  =  5

 

It takes  5  hours to break even.