Question

If the sum of three consecutive integers is 24, what is the middle integer?

• A. 7
• B. 8
• C. 9
• D. 10

Hint:

For consecutive integers, use n-1, n, n+1 and solve for n.

Answer 1

The Correct Option is B

To solve the problem of finding the middle integer of three consecutive integers whose sum is 24, we start by defining our variables. Let the three consecutive integers be \(x\), \(x+1\), and \(x+2\). The sum of these integers is:

\[x + (x+1) + (x+2) = 24\]

Combine like terms:

\[3x + 3 = 24\]

Subtract 3 from both sides:

\[3x = 21\]

Divide each side by 3:

\[x = 7\]

The integers are 7, 8, and 9. Therefore, the middle integer is \(8\).