Question

The sum of two numbers is 43 and the difference is 15. What is the larger and smaller numbers?

Answer 1

The answer to a "sum and difference" problem is that the larger number is the average of those given: (43 +15)/2 = 29.

The smaller number can be computed any of several ways, but subtracting the difference works: 29 -15 = 14

The larger number is 29.
The smaller number is 14.

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You can let the numbers be a and b, and let the sum and difference be s and d. Then you have
.. a + b = s
.. a - b = d
Add these two equations, and you find "b" is eliminated:
.. 2a = s + d

.. a = (s + d)/2 . . . . . . the average of the sum and difference
.. b = a - d . . . . . . . . . from the second equation

This solution is generic. Even if you have to "show work" on such a problem, you can use this known result to check your work.