The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.

Let x be the larger number and y the smaller number. Their sum and difference give the system x + y = 82 and x − y = 24. Add the equations to eliminate y: 2x = 106, so x = 53; then y = 82 − 53 = 29. The numbers are 53 and 29, matching choice D.

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