Answer
At most\[1280\]Miles
Work Step by Step
Let x be the number of miles driven.
The cost of travelling x miles would be,
\[80+0.25x\]
Now, the budget constraint gives rise to the following inequality:
\[80\,+0.25\text{x}\,\le \text{400}\]
This can be solved as follows:
\[\begin{align}
& 80+0.25x\le 400 \\
& 80+0.25x-80\le 400-80 \\
& 0.25x\le 320 \\
& \frac{0.25x}{0.25}\le \frac{320}{0.25}
\end{align}\]
\[x\le 1280\]
The number of miles travelled for the week can be at most 1280.
