Question

Joe's Taxi charges a total of $11 for a four-mile ride and a total of $23 for a ten-mile ride. The total charge is made up of an initial charge to hire the cab and a charge per mile driven. Find the initial charge to hire the cab.

Answer 1

Explanation:

Let x be the initial charge and y be the charge per mile driven.

We can write a system of equations:

$\begin{gathered} 11=x+4y \\ 23=x+10y \end{gathered}$

Using the elimination method we can find y easily:

$\begin{gathered} 11=x+4y \\ - \\ \frac{23=x+10y}{-12=-6y} \end{gathered}$

Solving for y:

$\begin{gathered} 6y=12 \\ y=\frac{12}{6}=2 \end{gathered}$

y = 2 is the charge per mile driven. Replacing this into any of the equations we can find the initial charge x:

$\begin{gathered} 11=x+4\cdot2 \\ 11=x+8 \\ x=11-8=3 \end{gathered}$

Answer:

The inital charge is $3