The sum of three consecutive integers is 174. What are the​ integers?

Let the three consecutive integers be \( n \), \( n+1 \), and \( n+2 \).

The sum of these integers can be expressed as:

\[
n + (n+1) + (n+2) = 174
\]

Simplifying the equation:

\[
3n + 3 = 174
\]

Subtract 3 from both sides:

\[
3n = 171
\]

Divide both sides by 3:

\[
n = 57
\]

So, the three consecutive integers are:

\[
57, 58, \text{ and } 59
\]

Would you like more details or have any questions?

Here are some related questions:
1. What if the sum of four consecutive integers is 174?
2. How would the solution change if the integers were consecutive even numbers?
3. What are the three consecutive integers if their sum is 201?
4. How can you express the sum of any three consecutive integers in a general form?
5. What is the product of the three consecutive integers found?

**Tip:** When solving for consecutive integers, always express them in terms of a single variable to simplify the equation.

Discover how to find three consecutive integers whose sum is 174 with a step-by-step solution. This problem involves integer arithmetic and solving linear equations. Suitable for students in Grades 7-9.

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