Question

Find three consecutive odd intergers with a sum of 75

Answer 1

Let the three consecutive odd integers be represented as \( x \), \( x + 2 \), and \( x + 4 \).

To find the integers, we can set up the following equation based on the information given:

\[
x + (x + 2) + (x + 4) = 75
\]

Combining like terms:

\[
3x + 6 = 75
\]

Now, subtract 6 from both sides:

\[
3x = 69
\]

Next, divide both sides by 3:

\[
x = 23
\]

Now we can find the three consecutive odd integers:

- The first integer: \( x = 23 \)
- The second integer: \( x + 2 = 25 \)
- The third integer: \( x + 4 = 27 \)

Thus, the three consecutive odd integers are **23, 25, and 27**.

To verify, their sum is:

\[
23 + 25 + 27 = 75
\]

So the solution is confirmed. The three consecutive odd integers are **23, 25, and 27**.