The problem asks to find the greatest of four consecutive integers whose sum is 214.

1. Problem Description

The problem asks to find the greatest of four consecutive integers whose sum is

2

1

4.

2. Solution Steps

Let $n$ be the smallest of the four consecutive integers. Then the other three integers are $n+1$, $n+2$, and $n+3$.

The sum of these four integers is given as

2

1

4. So we can write the equation:

$n + (n+1) + (n+2) + (n+3) = 214$

Combining like terms, we have:

$4n + 6 = 214$

Subtracting 6 from both sides of the equation, we get:

$4n = 214 - 6$

$4n = 208$

Dividing both sides by 4, we find the value of $n$:

$n = \frac{208}{4}$

$n = 52$

The four consecutive integers are 52, 53, 54, and

5

5. The greatest of these four integers is $n+3$, which is $52 + 3 = 55$.

3. Final Answer

55