The average of w and x is , and we want to go from to something like w+x. To do that we need to put the and over a common denominator. Multiply the by and the by . (Remember that we can multiply the numerator and denominator by the same number because a number divided by itself is equal to 1.) Now we can combine the terms: .
We know that wx = y from the problem, so we can replace the denominator with y. Now we have a y in the denominator on both sides, so we multiply both sides by y and get 4x + 4w = 4. Finally, divide every term by 4, and we get x + w = 1. Put 1 in the numerator of the average, and we get the answer.
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