The sum of three consecutive even integers is 102. What is the value of the smallest integer in this group?

The correct answer is 32.

Step-by-Step Explanation:

Let the three consecutive even integers be represented as $x$, $x+2$, and $x+4$, where $x$ is the smallest even integer.

According to the given problem, the sum of these three consecutive even integers is 102. We can set up the algebraic equation as follows:

$x+(x+2)+(x+4)=102$

Combine the like terms on the left side of the equation:

$3x+6=102$

Subtract 6 from both sides of the equation to isolate the term with $x$:

$3x=102-6$

$3x=96$

Divide both sides by 3 to find the value of $x$:

$x=\frac{96}{3}$

$x=32$

Thus, the smallest integer in this group is 32.