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

Step-by-step 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 \\ - \\ (23=x+10y)/(-12=-6y) \end{gathered}`

Solving for y:

`\begin{gathered} 6y=12 \\ y=(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