Question

Two taxi companies compete in the same neighborhood. One of these companies
charges $2 for the taxi drop plus $1.20 for each mile driven, while the other charges $1
for the taxi drop, plus $1.40 for each mile driven.

a. Express these relationships as an algebraic system, where m represents miles
driven and c represents cost.

b. Solve the system.

Answer 1

Let m = miles

let c = cost

Create a system of equations.

taxi company 1: c = $1.20m + $2

taxi company 2 c = $1.40m + $1

Set both equations equal to each other to solve for variable m.

$1.20m + $2 = $1.40m + $1

Subtract $1.20 from both sides and Subtract $1 from both sides.

$1 = $0.20m.

Divide each side by $0.20.

5 = m.

Plug 5 into one of our original equations for m.

c = $1.20(5) + $2.

Simplify the right side of the equation

c = $8

In conclusion, c = $8 and m = 5