Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Mr. Jordan is contemplating which chauffeured car service to take to the airport. The first costs $17 up front and $1 per kilometer. The second costs $2 plus $2 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?​

Answer 1

To find the distance and total fare for the two car services, we can set up a system of equations. Solving the system will give us the answers. The distance at which both companies charge the same fare is 15 kilometers, and the total fare for that distance is $32.

Step-by-step explanation:

To write a system of equations for this situation, let's assume the driving distance is represented by a variable, 'd'.

The total fare for the first car is $17 up front plus $1 per kilometer which can be represented as 17 + 1d.

The total fare for the second car is $2 up front plus $2 per kilometer which can be represented as 2 + 2d.

To find the distance at which the two companies charge the same total fare, we can set the two expressions equal to each other:

17 + d = 2 + 2d

Now solve for 'd' to find the distance:

d = 15 kilometers

The total fare can be found by substituting the distance 'd' into one of the expressions:

Total fare = 17 + 1d = 17 + 1(15)

= 17 + 15

= $32