Summer Problem Solving Marathon Solution #1

Let x and y be the two numbers. Then we are told x + y = 10, and xy = 20. We want to find ¹⁄_x + ¹⁄_y.

Converting both fractions to the common denominator xy, we get ^y⁄_xy + ^x⁄_xy, or ^(x+y)⁄_xy.

Substituting our starting values for x + y and xy, we have ¹⁰⁄₂₀, or ¹⁄₂.

[Put any questions, objections, or alternative solutions in the comments.]