Answer
$(500,42500)$.
This means that when we sold or produced $500$ calculators, both cost and revenue are $\$42,500$.
Work Step by Step
The given functions are
$C(x)=22,500+40x$ and $R(x)=85x$
The break-even point is the intersection point of cost and revenue lines.
At the break even point both functions are equal.
$\Rightarrow R(x)=C(x)$.
Substitute both values and solve for $x$.
$\Rightarrow 85x=22,500+40x$
Subtract $40x$ from both sides.
$\Rightarrow 85x-40x=22,500+40x-40x$
Simplify.
$\Rightarrow 45x=22,500$
Divide both sides by $45$.
$\Rightarrow \frac{45x}{45}=\frac{22,500}{45}$
Simplify.
$\Rightarrow x=500$
Plug $x=500$ into cost function.
$\Rightarrow 22,500+40(500)$.
Simplify.
$\Rightarrow 22,500+20000$.
$\Rightarrow 42,500$.
Hence, the break-even point is $(500,42500)$.
This means that when we sold or produced $500$ calculators, both cost and revenue are $\$42,500$.
