Q31. - Algebra 2

Question

For exercises 31 and 32, define a variable, write an equation or inequality, and solve the problem.

31. Mrs. Denney is renting a car that gets 35 miles per gallon. The rental charge is $\mathbf{\backslash (}\mathbf{19}\mathbf{.}\mathbf{50}$ a day plus $\mathbf{18}\mathbf{\backslash }\mathbf{notc}$ per mile. Her company will reimburse her for $\mathbf{\backslash )}\mathbf{33}$ of this portion of her travel expenses. If Mrs. Denney rents the car for 1 day, find the maximum number of miles that will be paid for by her company.

Step-by-Step Solution

Answer

The maximum number of miles that will be paid for by her company is 75 miles.

Step 1 – Description of step.

As per the given information, rental charge of a car is $\$19.50$ for a day and charge per mile is $18\cancel{c}$.

 

Let m be the number of miles travelled. Amount reimbursed by company for her travel expanses is $\$33$.

Step 2 – Description of step.

Write an equation using given equation.

$19.5+0.18m=33$

Step 3 – Description of step.

Subtract $19.5$ from both the sides of the equation obtained in step 3.

$\begin{array}{c}19.5+0.18m-19.5=33-19.5\\ 0.18m=13.5\end{array}$

Step 4 – Description of step.

Divide each side of the equation in step 3 by $0.18$.

$\begin{array}{c}\frac{0.18m}{0.18}=\frac{13.5}{0.18}\\ m=75\end{array}$

 

Therefore, the maximum number of miles that will be paid for by her company is 75 miles.