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.