Find the two numbers that have a difference of 3 and a sum of 27.

The larger one is (27+3)/2 = 15.
The smaller one is 3 less, 12.

The two numbers are 12 and 15.


This is what I call a "sum and difference" problem. You are given the sum of two numbers and the difference between them. Since you see this kind of problem many times and many ways in Algebra courses, it can be worthwhile to remember the solution--or at least, the derivation of the solution.

Let "a" and "b" represent the numbers. Let "s" and "d" represent their sum and difference, respectively. You are given
.. a +b = s
.. a -b = d
Add these two equations.
.. 2a = (s +d)
Divide by 2.
.. a = (s +d)/2 . . . . . . . . . one of the numbers, as computed above

If you subtract the second equation from the first, you get
.. 2b = s -d
.. b = (s -d)/2 . . . . . . . . . the other number

Of course, you also know
.. b = s -a
.. b = a -d
.. a = s -b
.. a = b +d
so that once you have found either of the numbers, you have several ways to find the other one.

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