Question

Find three consecutive even integers, whose sum is 174 n+ n+2 n+4=174

Answer 1

Let's represent the three consecutive even integers using the variable \( n \):

1. The first integer: \( n \)
2. The second integer: \( n + 2 \)
3. The third integer: \( n + 4 \)

According to the problem, their sum is 174:

\[
n + (n + 2) + (n + 4) = 174
\]

Now, let's simplify the equation:

\[
n + n + 2 + n + 4 = 174
\]

Combining like terms:

\[
3n + 6 = 174
\]

Next, subtract 6 from both sides:

\[
3n = 174 - 6
\]
\[
3n = 168
\]

Now, divide by 3:

\[
n = \frac{168}{3} = 56
\]

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

1. First integer: \( n = 56 \)
2. Second integer: \( n + 2 = 56 + 2 = 58 \)
3. Third integer: \( n + 4 = 56 + 4 = 60 \)

Therefore, the three consecutive even integers are:

\[
\boxed{56}, \boxed{58}, \boxed{60}
\]