Question

Fernando just got his commercial driver's license and is starting a new career as a truck driver. Getting trained and licensed involved a one-time cost of $485. Gas and insurance end up costing him $2 per kilometer. For his first delivery, Fernando will get paid $370 plus $3 per kilometer that he drives. If he drives a certain distance on this delivery, Fernando will break even, making back all the money he had to spend. What distance would he have to drive? How much would both the costs and the earnings be? If Fernando drives __ kilometers, the costs and the earnings would both be $__.

Answer 1

Fernando needs to drive 115 kilometers to break even, at which point both his costs and earnings would be $725.

Step-by-step explanation:

To determine the distance Fernando needs to drive to break even, we need to set up an equation where his total earnings equal his total costs. His fixed cost for training and licensing is $485. His variable costs for gas and insurance are $2 per kilometer. His earnings are a fixed $370 plus $3 per kilometer.

Let x represent the number of kilometers Fernando needs to drive. The break-even equation will be:

485 + 2x = 370 + 3x

We solve for x by first subtracting 2x from both sides of the equation:

485 = 370 + x

Now, subtract 370 from both sides to find the number of kilometers:

x = 485 - 370

x = 115 kilometers

Therefore, Fernando needs to drive 115 kilometers to break even. At this point, both his costs and earnings will be:

Costs: 485 + (2 × 115) = $725

Earnings: 370 + (3 × 115) = $725

If Fernando drives 115 kilometers, the costs and the earnings would both be $725.