If the sum of three consecutive integers is 81, what are the integers?

To solve the problem, we need to understand how to represent three consecutive integers mathematically. We can denote the first integer as ( n ), making the next two integers ( n+1 ) and ( n+2 ). The sum of these three integers can be expressed as:

[

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

]

We know from the problem that this sum equals 81. Thus, we can set up the equation:

[

3n + 3 = 81

]

To isolate ( n ), we first subtract 3 from both sides:

[

3n = 81 - 3

]

[

3n = 78

]

Next, we divide both sides by 3:

[

n = \frac{78}{3} = 26

]

Now that we have ( n ), we can find the three consecutive integers:

[

n = 26, \quad n + 1 = 27, \quad n + 2 = 28

]

So, the consecutive integers are 26, 27, and 28. This matches the integers given