Question

What is the break-even point? How do we find it?

Answer 1

The break-even point is the point in which revenue equals cost.

Based on the question, our revenue = 45x and cost = 15x + 150.

If revenue = cost, we can form the following equality:

`45x=15x+150`

Then, we can now solve for x.

Subtract 15x on both sides of the equation.

`\begin{gathered} 45x-15x=15x-15x+150 \\ 30x=150 \end{gathered}`

Divide both sides by 30.

`\begin{gathered} (30x)/(30)=(150)/(30) \\ x=5 \end{gathered}`

The value of x is 5. At x = 5, the revenue and cost is:

`\begin{gathered} 45x=15x+150 \\ 45(5)=15(5)+150 \\ 225=75+150 \\ 225=225 \end{gathered}`

The revenue and cost are both $225 dollars.

Hence, the break even point is at (5, 225).