To solve the equation \( 724.67 + 488.75 + 743.27 \), we can add the numbers together step by step.
First, add the first two numbers: \[ 724.67 + 488.75 = 1213.42 \]
Next, add the result to the third number: \[ 1213.42 + 743.27 = 1956.69 \]
Thus, the solution is: \[ \boxed{1956.69} \]