The sum of two consecutive odd integers is 156. What is the larger integer?

The Sum of Two Consecutive Odd Integers Is 156. What Is the Larger Integer?

If you’ve ever wondered how to solve a simple yet interesting math puzzle, the sum of two consecutive odd integers offers a clear and logical solution. Understanding how to work with consecutive odd numbers not only sharpens basic algebra skills but also reveals the beauty of patterns in numbers.

What Are Consecutive Odd Integers?

Understanding the Context

Consecutive odd integers are two odd whole numbers that follow one after another—each differing by exactly 2. For example, 1 and 3, 5 and 7, or 43 and 45 are consecutive odd integers. Unlike even integers, which skip one number (e.g., 2, 4, 6), odd integers always follow a consistent step of two.

Setting Up the Problem

Let’s denote the first odd integer as:
x

Since the integers are consecutive and both odd, the next odd integer is:
x + 2

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Key Insights

According to the problem, their sum equals 156:
x + (x + 2) = 156

Solving the Equation

Combine like terms:
2x + 2 = 156

Subtract 2 from both sides:
2x = 154

Divide both sides by 2:
x = 77

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Final Thoughts

So, the smaller odd integer is 77.
The next consecutive odd integer is:
77 + 2 = 79

Verifying the Solution

Check the sum:
77 + 79 = 156 ✔️
Both numbers are odd and consecutive ✔️

Final Answer

The larger of the two consecutive odd integers is 79.

Why This Problem Matters

This classic problem helps reinforce foundational algebraic thinking—identifying variables, forming equations, and solving step-by-step. Whether you're teaching math, preparing for a quiz, or simply exploring number patterns, knowing how to find consecutive odd integers that sum to a specific total is a practical and insightful skill.

Next time you see a similar question, break it down like this: define the two numbers based on their odd continuity, set up a simple equation, and solve fast and confidently!

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Meta Description:
Learn how to find two consecutive odd integers that add up to 156. This tutorial shows step-by-step how to set up and solve the equation, leading to the larger integer of 79. Ideal for math students and problem solvers.