Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Mr. Long is contemplating which chauffeured car service to take to the airport. The first costs $3 up front and $4 per mile. The second costs $19 plus $2 per mile. For a certain driving distance, the two companies charge the same total fare. What is the distance? What is the total fare?

Answer 1

Considering the form:

`y=mx+b`

where y is the variable that depends on x, m changes depending on the value of x, and b is constant.

Then, in our problem:

• y ,is the cost of the chauffeured car service for both equations.

,

• x ,is the miles traveled.

,

• m ,is 4 in the first and 2 in the second.

,

• b ,is 3 in the first and 19 in the second.

Then, replacing the latter we can build our equations.

• Equation 1 ,(first service)

`y=4x+3`

• Equation 2 ,(second service)

`y=2x+19`

Solving the system of equations by substitution.

0. Replacing ,Equation 2 ,in equation ,1,:

`y=4x+3`
`2x+19=4x+3`

2. Grouping similar terms and solving for x

`19-3=4x-2x`
`16=2x`
`x=(16)/(2)`
`x=8`

3. Replacing this value in Equation 2 to get y:

`y=2\cdot8+19`
`y=16+19`
`y=35`

Answer: at 5 miles the two companies charge the same total fare of $35.