Question

I am trying to understand how to setup this equation!

Answer 1

We know that x represents the number of trips to the airport, and y represents the number of trips from the airport. If the taxi driver had 18 fares in total, then we can express the first equation.

`x+y=18`

The price of a ride to the airport is $3.50 and from the airport is $9, if the driver collected $118 for the day, then we can express the second equation.

`3.50x+9y=118`

In order to solve this system of equations, let's solve the first equation for x.

`x=18-y`

Then, we combine it with the second equation.

`\begin{gathered} 3.50(18-y)+9y=118\Rightarrow63-3.50y+9y=118\Rightarrow5.5y=118-63 \\ 5.5y=55\Rightarrow y=(55)/(5.5)\Rightarrow y=10 \end{gathered}`

Once we have the value of one variable, we can easily find the value of the other one.

`x=18-10=8`

Therefore, the coordinated pair that represents the solution is (8,10).