## Total Reciprocals

Find the sum of the reciprocals of two real numbers, given that these numbers have a sum of 150 and a product of 40.
Source: mathcontest.olemiss.edu 7/9/2007

SOLUTION
Let $x\textup{ and }y$ be two real numbers. Then,

$\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}$
$=\frac{150}{40}$
$=\frac{15}{4}$

Answer: $\frac{15}{4}$.