Break-Even Analysis for Gadget Sales

When a company produces and sells gadgets, it incurs both fixed and variable costs. The fixed costs of the company amount to $1,800, while the variable cost per gadget is $40. The company sells each gadget for $100.

Let $x$ represent the number of gadgets sold. The total cost and total revenue can be expressed with the following equations:

$$ ext{Total Cost} = 1800 + 40x$$

$$ ext{Total Revenue} = 100x$$

To find the break-even point, where total costs equal total revenue, solve the equation:

$$1800 + 40x = 100x$$

Determine the value of $x$ at which the company breaks even by solving this equation.