Three consecutive odd integers have a sum of 27 . Find the integers.


Let the three consecutive odd integers be represented as:

- \( x \) (the first integer),
- \( x + 2 \) (the second integer), 
- \( x + 4 \) (the third integer).

The sum of these integers is given as:

\[
x + (x + 2) + (x + 4) = 27
\]

Now, simplify the equation:

\[
x + x + 2 + x + 4 = 27
\]

\[
3x + 6 = 27
\]

Subtract 6 from both sides:

\[
3x = 21
\]

Now, divide by 3:

\[
x = 7
\]

So, the first integer is 7. The other two integers are:

\[
x + 2 = 7 + 2 = 9
\]
\[
x + 4 = 7 + 4 = 11
\]

Thus, the three consecutive odd integers are **7, 9, and 11**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the sum of three consecutive even integers if the smallest is 8?
2. If the sum of three consecutive odd integers is 45, what are the integers?
3. Can you find three consecutive numbers whose sum is 78?
4. What is the formula for finding the sum of \( n \) consecutive odd integers?
5. How does the sum of three consecutive even integers compare to three consecutive odd integers?

**Tip:** Consecutive odd integers always differ by 2.

Three consecutive odd integers have a sum of 27. Find the integers.

Solve the algebraic problem of finding three consecutive odd integers that sum up to 27. This step-by-step solution involves linear equations and basic algebra, perfect for students in Grades 6-8.

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