To find Juan’s hourly rate before his raise, we can let \( r \) represent his old hourly rate. Based on the information given, we know that he received a $0.50 raise and that his new hourly rate is $10.25. The equation can be set up as follows:
\[ r + 0.50 = 10.25 \]
Now, to solve for \( r \), we subtract $0.50 from both sides:
\[ r = 10.25 - 0.50 \]
Calculating this gives:
\[ r = 9.75 \]
Thus, Juan's hourly rate before his raise was $9.75.
The correct equation and solution from the given options is:
\( r + 0.50 = 10.25: \) Subtract .50 from both sides. The answer is $9.75.