Question

Warren 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 $500. Gas and insurance end up
costing him $4 per mile. For his first delivery, Warren will get paid $400 plus $8 per mile that
he drives. If he drives a certain distance on this delivery, Warren will break even, making
back all the money he had to spend. How much would both the costs and the earnings be?
Write a system of equations, graph them, and type the solution.
1,000
Dollars ($)
800
600
400
200
0
3
10
20
30
40
50

Answer 1

The solution to the system of equations is (m = 25), and the total costs and earnings at this distance will be $600.

To solve this problem, we can set up a system of equations to represent the costs and earnings for Warren's first delivery. Let's use the variable (m) to represent the distance in miles that Warren drives on his first delivery.

The total cost (C) for the delivery is the sum of the one-time cost for training and licensing, and the cost for gas and insurance. The total earnings (E) for the delivery is the sum of the base payment and the payment for the distance driven.

The system of equations is as follows:

[ C = 500 + 4m ]

[ E = 400 + 8m ]

To find the distance at which Warren will break even, we can set the cost equal to the earnings and solve for (m):

[ 500 + 4m = 400 + 8m ]

[ 100 = 4m ]

[ m = 25 ]

So, Warren will break even if he drives 25 miles on his first delivery. At this distance, the total cost and total earnings will both be $600.

Therefore, the solution to the system of equations is (m = 25), and the total costs and earnings at this distance will be $600.