### Instruction: 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).### Response: 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 $x = 31$.