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:
[tex]45x=15x+150[/tex]
Then, we can now solve for x.
Subtract 15x on both sides of the equation.
[tex]\begin{gathered} 45x-15x=15x-15x+150 \\ 30x=150 \end{gathered}[/tex]
Divide both sides by 30.
[tex]\begin{gathered} \frac{30x}{30}=\frac{150}{30} \\ x=5 \end{gathered}[/tex]
The value of x is 5. At x = 5, the revenue and cost is:
[tex]\begin{gathered} 45x=15x+150 \\ 45(5)=15(5)+150 \\ 225=75+150 \\ 225=225 \end{gathered}[/tex]
The revenue and cost are both $225 dollars.
Hence, the break even point is at (5, 225).
