The sum of three consecutive integers is 72. What is the largest integer?
["The Sum of Three Consecutive Integers Is 72 – What Is the Largest Integer?", "When faced with a puzzle like “the sum of three consecutive integers is 72. What is the largest integer?”, many people initially pause—but solving it reveals the elegant power of algebra and number logic. In this SEO-optimized guide, we’ll explore how to determine the largest of three consecutive integers that add up to 72, making this problem a classic example of both math and critical thinking.", "---", "### What Are Consecutive Integers?", "Consecutive integers are numbers that follow one after another in order without gaps. For example, 5, 6, and 7 are three consecutive integers. If we let the middle integer be ( x ), then the three consecutive integers can be written as:", "- First: ( x - 1 )\n- Middle: ( x )\n- Last: ( x + 1 )", "---", "### Step-by-Step: Setting Up the Equation", "To find the sum of these three numbers, we simply add them:", "[\n(x - 1) + x + (x + 1) = 72\n]", "Simplify the left side:", "[\nx - 1 + x + x + 1 = 3x\n]", "So the equation becomes:", "[\n3x = 72\n]", "---", "### Solving for ( x )", "Divide both sides by 3:", "[\nx = \frac{72}{3} = 24\n]", "Thus, the middle integer is 24.", "---", "### Finding the Largest Integer", "Since the integers are consecutive, the largest is simply:", "[\nx + 1 = 24 + 1 = 25\n]", "---", "### Verifying the Solution", "Let’s double-check:", "- 23 + 24 + 25 = 72 ✅\n- The sum is correct\n- The largest integer is indeed 25 ✅", "---", "### Why This Problem Matters (SEO Focus)", "Understanding how to break down word problems into mathematical expressions is a key skill in algebra and elementary math education. This problem illustrates:", "- How to define variables for unknown quantities\n- Simplify expressions using algebraic rules\n- Solve linear equations efficiently\n- Apply logic to verify solutions", "These concepts are foundational not only for school math but for real-world problem-solving in everyday life, science, technology, and more.", "---", "### Final Answer Summary", "- The three consecutive integers are 23, 24, and 25\n- Their sum: ( 23 + 24 + 25 = 72 )\n- The largest integer is 25", "---", "### Want to Master Integer Problems Like This?", "Explore more algebra practice problems—especially word equations—to strengthen your math confidence. Use keywords like “consecutive integers algebra,” “solve three consecutive integers sum,” and “how to find largest integer from sum” for better SEO visibility and deeper learning.", "---", "Key Takeaways:\n✔ Middle term = 24 → Next integer is 25\n✔ Easy setup using ( x - 1, x, x + 1 )\n✔ Quick verification confirms the answer\n✔ This problem builds core algebra skills", "---", "Ready to tackle your next math challenge? Start with the basics—consecutive integers—and watch your problem-solving grow!", "Keywords: consecutive integers sum 72, largest of three consecutive integers, algebra problem solution, integer arithmetic, step-by-step math tutorial"]
