The sum of two numbers is 50, and their difference is 12. What are the two numbers?
["The Sum and Difference of Two Numbers: Solving a Classic Math Problem", "Mathematics often presents us with engaging puzzles that help sharpen logical thinking — and one of the simplest yet profound challenges is solving for two numbers given their sum and difference. This article explores a classic problem: The sum of two numbers is 50, and their difference is 12. What are the two numbers? Whether you're a student mastering algebra or a lifelong learner brushing up on basic math, this problem offers a clear, step-by-step solution using simple algebraic reasoning.", "---", "### Understanding the Problem", "We are told:\n- The sum of two numbers is 50.\n- The difference between the same two numbers is 12.", "Let the two unknown numbers be ( x ) and ( y ), where ( x > y ). From the problem, we form two key equations:", "1. ( x + y = 50 )\n2. ( x - y = 12 )", "Our goal is to find the values of ( x ) and ( y ) using these equations.", "---", "### Step-by-Step Solution", "Step 1: Write both equations clearly\n[\n\begin{cases}\nx + y = 50 \quad \ ext{(Sum)} \\nx - y = 12 \quad \ ext{(Difference)}\n\end{cases}\n]", "Step 2: Add the two equations to eliminate ( y )\nAdding the left sides: ( x + y + x - y = 2x )\nAdding the right sides: ( 50 + 12 = 62 )\nSo,\n[\n2x = 62\n]\nDivide both sides by 2:\n[\nx = 31\n]", "Step 3: Substitute ( x ) into one of the original equations\nUsing the sum equation ( x + y = 50 ):\n[\n31 + y = 50\n]\nSubtract 31 from both sides:\n[\ny = 50 - 31 = 19\n]", "---", "### Verifying the Solution", "Check that the numbers satisfy both conditions:\n- Sum: ( 31 + 19 = 50 ) ✅\n- Difference: ( 31 - 19 = 12 ) ✅", "Both conditions are met, confirming our solution is correct.", "---", "### Final Answer", "The two numbers are:", "- 31\n- 19", "---", "### Why This Problem Matters in Math Education", "This type of problem is foundational in algebra. It teaches:\n- How to translate word problems into mathematical equations.\n- The use of systems of equations in a straightforward context.\n- Logical steps to isolate variables and solve for unknowns.", "Even though this example is simple, it builds the critical thinking skills needed for more complex algebraic challenges.", "---", "### Summary", "Given:\n- Sum: 50\n- Difference: 12", "Using the system:\n[\n\begin{align}\nx + y &= 50 \\nx - y &= 12 \\n\end{align}\n]\nWe found:\n[\nx = 31,\quad y = 19\n]", "The two numbers are 31 and 19.", "---", "### Want to Practice More?", "Explore problems like:\n- Two numbers differ by 8 and sum to 44\n- The sum of two numbers is 72, and one is double the other\n- Use variables and equations to solve real-life scenarios", "Mastering these builds confidence and precision in mathematics.", "---", "Keywords:\nsum of two numbers is 50, difference of two numbers is 12, solve two equations, algebra problem, bedtime math, math practice, basics of algebra, how to find two numbers given sum and difference", "Meta Description:\nDiscover how to find two numbers when their sum is 50 and difference is 12. Solve step-by-step with algebra examples suitable for students and math learners."]
