If two consecutive integers sum to 57, what is the average of the two integers?

If two consecutive integers sum to 57, what is the average of the two integers?

• A. 28
• B. 28.5
• C. 29
• D. 28.0

Answer: (B)

The average of two numbers is half their sum. Here the two consecutive integers add up to 57, so their average is 57/2 = 28.5. If you want the actual numbers, let the smaller be n; then n + (n+1) = 57 gives 2n + 1 = 57, so n = 28. The pair is 28 and 29, and their average is (28 + 29)/2 = 28.5. Noting that 28 would correspond to a total of 56 and 29 to a total of 58 helps confirm why 28.5 is the correct average for a sum of 57.

The average of two numbers is half their sum. Here the two consecutive integers add up to 57, so their average is 57/2 = 28.5. If you want the actual numbers, let the smaller be n; then n + (n+1) = 57 gives 2n + 1 = 57, so n = 28. The pair is 28 and 29, and their average is (28 + 29)/2 = 28.5.

Noting that 28 would correspond to a total of 56 and 29 to a total of 58 helps confirm why 28.5 is the correct average for a sum of 57.