If the sum of three consecutive integers is 99, what is the smallest integer?

To find the smallest integer of three consecutive integers that sum up to 99, you can start by letting the three consecutive integers be represented as ( n ), ( n+1 ), and ( n+2 ). The sum of these integers can be expressed algebraically:

[

n + (n + 1) + (n + 2) = 99

]

Combining like terms results in:

[

3n + 3 = 99

]

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

[

3n = 99 - 3

]

[

3n = 96

]

Next, divide both sides by 3 to solve for ( n ):

[

n = \frac{96}{3}

]

[

n = 32

]

Thus, the three consecutive integers are 32, 33, and 34. Among these, the smallest integer is 32.

Therefore, the answer is 32, confirming that this approach effectively identifies the correct solution based on the properties of consecutive integers and their algebraic representation through equations.