The sum of two numbers is 50, and their difference is 14. What is the larger number?
["# Solving the Mystery: The Sum and Difference of Two Numbers\nCan you find the larger number when the sum is 50 and the difference is 14?", "When faced with a classic math problem—two numbers whose sum is 50 and difference is 14—many wonder quickly how to identify the larger number. This is not just a routine equation; it’s a puzzle that blends algebra with logical thinking. In this article, we’ll walk through step-by-step how to solve this problem and show just why the larger number is 32.", "---", "## Understanding the Problem", "We are given two key pieces of information:\n- The sum of two numbers is 50\n- The difference between the same two numbers is 14", "Let’s define the two unknown numbers as x (the larger number) and y (the smaller number). Then:", "- Sum equation: x + y = 50\n- Difference equation: x − y = 14", "Our goal is to find x, the larger number.", "---", "## Step-by-Step Solution", "### Step 1: Add the Two Equations\nBy adding the sum and difference equations together, we eliminate the variable y:", "[\n(x + y) + (x - y) = 50 + 14\n]", "Simplifying:\n[\nx + y + x - y = 64\n\Rightarrow 2x = 64\n]", "### Step 2: Solve for x\nDivide both sides by 2:\n[\nx = \frac{64}{2} = 32\n]", "---", "## Verifying the Solution", "Let’s double-check by finding y using the sum equation:", "[\nx + y = 50\n\Rightarrow 32 + y = 50\n\Rightarrow y = 50 - 32 = 18\n]", "Check the difference:\n[\nx - y = 32 - 18 = 14 \quad \ ext{✓ Correct}\n]", "---", "## Why This Method Works", "This approach uses a well-known technique in algebra: combining equations to eliminate one variable. By adding sum and difference, we directly isolate and solve for the larger number without needing multiple steps or guesswork.", "---", "## Final Answer: The Larger Number is 32", "When the sum of two numbers is 50 and their difference is 14, the larger number is 32.", "This problem exemplifies how basic algebra helps solve everyday challenges—whether in math class, work, or real-life scenarios.", "---", "### Want to Practice More?", "Try solving other equations of the form:\n- Sum = ?\n- Difference = ?\nThen find the larger number using sum and difference.", "Understanding this pattern builds strong problem-solving skills and boosts your mathematical confidence!", "---", "Keywords: sum of two numbers 50, difference of two numbers, solve equations, algebra basics, find larger number, sum and difference problem, step-by-step math, math solution guide"]
