Answer to Question #231050 in Algebra for Vee

Question

One number is four times another number. Determine the two numbers of the sum of their reciprocals is 5/16

Answer 1

Let's take the two numbers to be $x$ and $y$

$x=4y\\\frac{1}{x}+\frac{1}{y}=\frac{5}{16}$

Substitute for $x$

$\frac{1}{4y}+\frac{1}{y}=\frac{5}{16}\\\frac{1+4}{4y}=\frac{5}{16}\\\frac{5}{4y}=\frac{5}{16}\\y=4\\x=4y\\x=4(4)\\x=16$