Q65. - Algebra 2

Question

For the exercise 65, define a variable, write an equation, and solve the problem.

 

CAR EXPENSES  Benito spent $\backslash (1837$ to operate his car last year. Some of these expenses are listed below. Benito’s only other expense was for gasoline. If he drove 7600 miles, what was the average cost of the gasoline per mile?

 

Operating expenses

 

Insurance: $\backslash )972$

Registration: $\backslash (114$

Maintenance: $\backslash )105$

Step-by-Step Solution

Answer

The required answer is $\$0.085$.

Step 1- Define the required variable

Consider x be the expense of gasoline. 

Step 2 – Form the equation

Take the variable and form the equation by using that the addition of all the expenses including gasoline will be equal to 1837.

 

$x+972+114+105=1837$

Step 3- Solve the equation for x

Write the obtained equation in simplified form.

 

$x+1191=1837$

 

Perform subtraction of 1191 from both sides of the equation.

 

$\begin{array}{c}x+1191-1191=1837-1191\\ =646\end{array}$

Step 4- Determine the average cost per mile

Divide the expense on gasoline by total miles of driving.

 

$\frac{646}{7600}=0.085$

 

The average cost of gasoline is $\$0.085$ per mile.

Step 5- Perform the checking

Determine the cost for 7600 miles. 

$0.085\times 7600=646$

Perform the addition between all the expenses including gasoline.

$646+972+114+105=1837$

This results in the provided price which means that the obtained answer is correct.