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The sum of three consecutive odd integers is 153 What is the value of the largest of the integers?

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

The sum of these three integers is given as:

\[
x + (x + 2) + (x + 4) = 153
\]

Simplify the equation:

\[
3x + 6 = 153
\]

Subtract 6 from both sides:

\[
3x = 147
\]

Now, divide both sides by 3:

\[
x = 49
\]

So, the three consecutive odd integers are \( 49 \), \( 51 \), and \( 53 \). The largest integer is:

\[
\boxed{53}
\]

Would you like a detailed breakdown or have any other questions?

Here are some related questions you can explore:
1. What if the sum was 195? What would the integers be?
2. How would the solution change if they were consecutive even integers?
3. What happens if you add four consecutive odd integers instead of three?
4. How can this method be applied to find five consecutive odd integers with a given sum?
5. How does solving for consecutive integers differ from solving for multiples of integers?

**Tip:** When dealing with consecutive odd or even integers, always represent them as \( x \), \( x+2 \), \( x+4 \), etc.

The sum of three consecutive odd integers is 153. What is the value of the largest of the integers?

Learn how to solve a problem involving three consecutive odd integers with a sum of 153. This algebraic problem introduces concepts like consecutive integers and basic linear equations. Suitable for students in Grades 6-8.

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