Question

the sum of three consecutive even integers is 162. What is the smallest of these integers?

Answer 1

Let's denote the three consecutive even integers as \( x \), \( x + 2 \), and \( x + 4 \).

The sum of these integers can be written as:
\[
x + (x + 2) + (x + 4) = 162
\]

Combining like terms gives us:
\[
3x + 6 = 162
\]

Next, we can subtract 6 from both sides:
\[
3x = 162 - 6
\]
\[
3x = 156
\]

Now, divide both sides by 3:
\[
x = \frac{156}{3} = 52
\]

Thus, the smallest of the three consecutive even integers is \( x = 52 \).

The three consecutive even integers are:
- \( 52 \)
- \( 54 \)
- \( 56 \)

So the smallest integer is:
\[
\boxed{52}
\]