The average of the numbers 23 and $x$ is 27. What is the positive difference between 23 and $x$? (Recall that the average of two numbers is their sum divided by 2).
To find $x$, I need to use the formula for the average of two numbers: $\frac{23 + x}{2} = 27$. Multiplying both sides by 2, I get $23 + x = 54$. Subtracting 23 from both sides, I get $x = 31$. The positive difference between 23 and 31 is $|23 - 31| = 8$.

