To solve the problem, we need to set up an equation based on the information provided.
Let's denote the number of miles Joe drove by [tex]\( x \)[/tex].
1. Each mile driven reimburses Joe [tex]$0.65. Therefore:
\[
\text{Reimbursement for miles driven} = 0.65x
\]
2. Joe also receives $[/tex]100 for lodging. Therefore, the total reimbursement Joe receives can be expressed as:
[tex]\[
\text{Total reimbursement} = 100 + 0.65x
\][/tex]
3. According to the problem, Joe's total reimbursement was $236.50. Hence, we can set up the following equation:
[tex]\[
100 + 0.65x = 236.50
\][/tex]
Now, let's solve this equation for [tex]\( x \)[/tex]:
4. Subtract 100 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
100 + 0.65x - 100 = 236.50 - 100
\][/tex]
Simplifying, we get:
[tex]\[
0.65x = 136.50
\][/tex]
5. To solve for [tex]\( x \)[/tex], divide both sides by 0.65:
[tex]\[
x = \frac{136.50}{0.65}
\][/tex]
6. Performing the division, we find:
[tex]\[
x = 210
\][/tex]
Therefore, Joe drove 210 miles.
