Write a system of equations to describe the situation below, solve

Question

using substitution, and fill in the blanks.
Mr. Solomon is contemplating which chauffeured car service to take
to the airport. The first costs $4 up front and $4 per mile. The
second costs $20 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

x = distance in miles

The first costs $4 up front and $4 per mile means:

The first costs = 4 + 4 x

The second costs $20 plus $2 per mile means:

The second costs = 20 + 2 x

For a certain driving distance, the two companies charge the same total fare means:

The first costs = The second costs

4 + 4 x = 20 + 2 x

Subtract 4 to both sides

4 x = 16 + 2 x

Subtract 2 x to both sides

2 x = 16

x = 16 / 2 = 8 miles

Check of result:

4 + 4 x = 20 + 2 x

4 + 4 ∙ 8 = 20 + 2 ∙ 8

4 + 32 = 20 + 16

36 = 36

Answer 2

The distance = 8 miles

The total fare = $36

Answer 3

x = miles driven for the two companies to have the same total fare

company 1: 4x(because it pays $4 per mile)
company 2: 2x (because it pays $2 per mile)

company 1: +4 (because it charges $4 up front)
company 2: +20(because it charges $20 up front)

equation would be:
4x + 4 = 20 + 2x

Isolate variable.

4 = 20-2x

-16 = -2x

x = 8

It takes 8 miles for the companies to pay the same total fare.

To figure out what the price was, plug in the value of x.
4(8) + 4 = 20 + 2(8)
32+4 = 20+16
36=36

Final Answer: The companies would both charge $36 in 8 miles.

Hope this helps!