Question

Mr. Clayton is contemplating which chauffeured car service to take to the airport. The first costs $5 up front and $4 per kilometer. The second costs $15 plus $3 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? Write a system of equations, graph them, and type the solution.______ kilometers

Answer 1

Given in the question:

a.) The first costs $5 upfront and $4 per kilometer.

b.) The second costs $15 plus $3 per kilometer.

Let's generate the equation of each of the car service charges,

Let,

y = total cost of service

x = distance traveled

a.) The first costs $5 upfront and $4 per kilometer.

$\text{ y = 5 + 4x}$

b.) The second costs $15 plus $3 per kilometer.

$\text{ y = 15 + 3x}$

Let's determine the driving distance when the two companies charge the same.

We get,

$y_{1st\text{ Company}}=y_{2nd\text{ Company}}_{}$$\text{ 5 + 4x = 15 + 3x}$$\text{ 4x - 3x = 15 - 5}$$\text{ x = 10}$

Therefore, the two companies charge the same at a driving distance of 10 kilometers.

Summary:

1. The system of equations.

y = 5 + 4x

y = 15 + 3x

2. The solution.

x = 10

3. Graphing the system of equations.