Question

Three consecutive integers have a sum of 228. What is the greatest of the 3 integers?

Answer 1

Let the three consecutive integers be represented as \( x \), \( x+1 \), and \( x+2 \).

The sum of these three integers can be expressed as:

\[
x + (x + 1) + (x + 2) = 228
\]

Simplifying the left side, we get:

\[
3x + 3 = 228
\]

Now, we can subtract 3 from both sides:

\[
3x = 228 - 3
\]

\[
3x = 225
\]

Next, we divide both sides by 3 to solve for \( x \):

\[
x = \frac{225}{3} = 75
\]

Thus, the three consecutive integers are:

\[
75, 76, \text{ and } 77
\]

The greatest of these integers is:

\[
\boxed{77}
\]

To verify, we can check the sum of these integers:

\[
75 + 76 + 77 = 228
\]

The sum is correct, confirming that the largest integer is indeed \( \boxed{77} \).