Question

One number is four times another number. the sum of their reciprocals is 1/4. what are the numbers?

Answer 1

Answer:

4/1 is the answer of the question

Answer 2

Answer:

Using the information from the question, one can construct two equations:

$4z = x$

$\frac{1}{z} + \frac{1}{x}$

by substituting (1) into (2) to find x

$\frac{1}{z} + \frac{1}{4z}$

$\frac{5}{4z} = \frac{1}{4}$

$\frac{4z}{5} = \frac{4}{1}$

$\frac{4z}{1} = \frac{20}{1}$

$z = \frac{20}{4}$

⇒ z = 5

By substituting value of z into (1)

⇒ 4 (5) = x

⇒ x = 20

Thus the two numbers are 5 & 20