The sum of three consecutive integers is 96. What is the largest integer?
["The Sum of Three Consecutive Integers Is 96. What Is the Largest Integer?", "Solving mathematical puzzles can be both fun and insightful. One common challenge many encounter is determining the largest of three consecutive integers when their total is known. In this article, we’ll explore how to find the largest integer when the sum of three consecutive integers equals 96.", "### What Are Consecutive Integers?", "Consecutive integers are numbers that follow each other in order without gaps — for example, 14, 15, and 16. We’re asked to find three consecutive integers whose sum is exactly 96, then identify the largest one.", "### Step-by-Step Solution", "1. Define the integers algebraically\n Let the first integer be ( x ).\n Then, the next two consecutive integers are ( x + 1 ) and ( x + 2 ).", "2. Set up the equation based on their sum\n The sum is:\n [\n x + (x + 1) + (x + 2) = 96\n ]", "3. Simplify the equation\n Combine like terms:\n [\n x + x + 1 + x + 2 = 96\n ]\n [\n 3x + 3 = 96\n ]", "4. Solve for ( x )\n Subtract 3 from both sides:\n [\n 3x = 93\n ]\n Divide by 3:\n [\n x = 31\n ]", "5. Identify the three integers\n The integers are:\n - First: 31\n - Second: 32\n - Largest: 33", "### Verification\nTo confirm:\n[\n31 + 32 + 33 = 96\n]\nThe sum matches, so the solution is correct.", "### Final Answer: The largest integer is 33.", "Understanding how to break down such problems using algebra not only helps in finding the answer but also strengthens problem-solving skills useful in real-life math applications. Remember, identifying consecutive integers by a simple variable and a linear equation makes these puzzles manageable!", "---", "Keywords: sum of three consecutive integers, largest integer 96, consecutive numbers solution, algebra problem, integer arithmetic\nMeta Description: Discover how to find the largest of three consecutive integers that sum to 96—step-by-step explanation with verified answer and practical insights."]
