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# How many hours does she break even?

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How do I set this up and work through it?

Feb 22, 2018

#1
+7612
+2

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.

Feb 22, 2018

#1
+7612
+2

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.

hectictar Feb 22, 2018