Chapter 4.6, Problem 44E

To determine

To find:The minimum numbers of miles per gallon that would fulfil Daniels criteria.

Answer to Problem 44E

The minimum number of miles is $25.7\text{mpg}$ .

Explanation of Solution

Given information:

Daniel drives $15,000\text{miles}$ each year. The car he wants to buy averages $20\text{miles}$ on one gallon of gasoline. He decided to buy another car if he could save at least $ $200$ per year in gasoline expense. Assuming gasoline costs $ $1.20$ per gallon.

Daniel drives $15,000\text{miles}$ . Let $x$ be a gallon of gas then,

  $\begin{array}{c}20=\frac{15,000}{x}\\ 20x=15,000\\ x=750\end{array}$

Given, the cost of gasoline is $ $1.20$ then,

  $750\times 1.20=900\text{}\text{}\text{gallons}$

Also,

  $\begin{array}{c}1.2x=900-200\\ x=583.33\text{gallons}\end{array}$

Now, the minimum number of miles per gallon is given by,

  $\frac{15,000}{583.33}=25.7\text{mpg}$ .

Therefore, the minimum number of miles is $25.7\text{mpg}$ .