If the sum of three consecutive integers is 72, what is the smallest integer?

To solve the problem, start by letting the three consecutive integers be represented as (n), (n + 1), and (n + 2). The sum of these integers can be expressed as:

[

n + (n + 1) + (n + 2) = 72

]

Simplifying this equation, we combine like terms:

[

3n + 3 = 72

]

Next, to isolate (n), subtract 3 from both sides:

[

3n = 69

]

Then, divide both sides by 3:

[

n = 23

]

Now, since (n) represents the smallest integer in the sequence, the smallest integer of the three consecutive integers is indeed 23.

This method shows how knowing the relationship between consecutive integers and their sum can directly lead you to the solution. The approach is systematic and relies on algebraic manipulation to arrive at the answer clearly and accurately.