To find out how many miles Luis jogged, we can set up the equation based on the information given. The amount of money raised is represented by the expression \(1.75m\) where \(m\) is the number of miles jogged.
We know that the total amount raised by Luis is $21. Therefore, we can set up the equation:
\[ 1.75m = 21 \]
To solve for \(m\), we can divide both sides of the equation by 1.75:
\[ m = \frac{21}{1.75} \]
Now, performing the division:
\[ m = 12 \]
Thus, the number of miles Luis jogged is \(\boxed{12}\).