The sum of three consecutive even integers is 186. What is the largest integer?
["The Sum of Three Consecutive Even Integers Is 186. What Is the Largest Integer?", "Finding the largest of three consecutive even integers whose total sum equals 186 is a classic algebra problem that confidently reveals how even numbers work together. Whether you're solving a math puzzle, teaching students, or sharpening your analytical skills, understanding this step-by-step can boost your confidence. In this article, we’ll break down how to identify the integers, solve the equation, and know exactly which is the largest.", "### Step 1: Define the Integers\nLet the three consecutive even integers be represented by:\n- First even integer: x\n- Second even integer: x + 2\n- Third even integer: x + 4", "Since they are consecutive even numbers, each number increases by 2 from the previous.", "### Step 2: Set Up the Equation\nTheir sum equals 186:\n[\nx + (x + 2) + (x + 4) = 186\n]", "### Step 3: Simplify and Solve\nCombine like terms:\n[\n3x + 6 = 186\n]\nSubtract 6 from both sides:\n[\n3x = 180\n]\nDivide by 3:\n[\nx = 60\n]", "### Step 4: Identify the Integers\nNow substitute back to find all three:\n- First: 60\n- Second: 60 + 2 = 62\n- Third (largest): 60 + 4 = 64", "### Step 5: Verify the Sum\nCheck the total:\n[\n60 + 62 + 64 = 186 \quad \ ext{(Correct!)}\n]", "### Final Answer\nThe largest of the three consecutive even integers is 64.", "---", "This straightforward approach proves how even numbers form an arithmetic sequence with a consistent difference. Once you master this method, solving similar problems—like sums of consecutive odd or even numbers—becomes intuitive. If you're studying math, testing word problems builds logical thinking and strengthens algebraic skills. So next time someone asks, “What’s the largest of three consecutive even integers summing to 186?” you’ll confidently say: “It’s 64!”"]
