The problem asks us to find three consecutive integers whose sum is 57.

1. Problem Description

The problem asks us to find three consecutive integers whose sum is

5

7.

2. Solution Steps

Let $n$ be the first integer. Then the next two consecutive integers are $n+1$ and $n+2$.

The sum of these three integers is $n + (n+1) + (n+2)$.

We are given that the sum is 57, so we can write the equation:

$n + (n+1) + (n+2) = 57$.

Combining like terms, we get:

$3n + 3 = 57$.

Subtract 3 from both sides:

$3n = 57 - 3$

$3n = 54$.

Divide both sides by 3:

$n = \frac{54}{3}$

$n = 18$.

The first integer is

1

8. The second integer is $n+1 = 18+1 = 19$.

The third integer is $n+2 = 18+2 = 20$.

We can check that $18 + 19 + 20 = 57$.

3. Final Answer

The three consecutive integers are 18, 19, and 20.