**Three consecutive integers add up to 51. What are these integers?**

To find the three consecutive integers that add up to 51, we can follow these steps:

1. **Define the consecutive integers:**

   Let's denote the three consecutive integers as \(x\), \(x + 1\), and \(x + 2\).

2. **Set up the equation:**

   According to the problem, the sum of these integers is 51. This can be written as:
   \[
   x + (x + 1) + (x + 2) = 51
   \]

3. **Simplify the equation:**

   Combine like terms to simplify the equation:
   \[
   x + x + 1 + x + 2 = 51
   \]
   \[
   3x + 3 = 51
   \]

4. **Solve for \(x\):**

   Subtract 3 from both sides of the equation to isolate the term involving \(x\):
   \[
   3x = 48
   \]

   Divide both sides by 3 to solve for \(x\):
   \[
   x = 16
   \]

5. **Determine the three consecutive integers:**

   The first integer is \(x = 16\). Therefore, the three consecutive integers are:
   \[
   16, 17, \text{ and } 18
   \]

6. **Check the solution:**

   To verify, calculate the sum of 16, 17, and 18:
   \[
   16 + 17 + 18 = 51
   \]
   Since the sum is indeed 51, our solution is correct.

So, the three consecutive integers are **16, 17, and 18**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What are consecutive integers, and how can they be represented algebraically?
2. How can you find four consecutive integers that sum up to a given number?
3. What if the sum of three consecutive even integers is given instead?
4. How do you solve equations involving consecutive odd integers?
5. Can you generalize a formula for the sum of any number of consecutive integers?

**Tip:** For problems involving consecutive integers, always remember that they differ by a fixed amount (usually 1 for integers or 2 for even/odd integers), which simplifies the setup of equations.

Discover how to find three consecutive integers that sum up to 51 with a step-by-step solution. This problem involves solving an integer equation using algebraic concepts, particularly focusing on consecutive integers. Suitable for students in Grades 7-9.

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