Respuesta :

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

[tex]4 z = x[/tex]  ...  (1)

[tex] \frac{1}{z} + \frac{1}{x} [/tex]   ... (2)

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

[tex] \frac{1}{z} + \frac{1}{4z} = \frac{1}{4} [/tex]

[tex]\frac{5}{4z} = \frac{1}{4} [/tex]

\frac{5}{4z}  =   \frac{1}{4}  

[tex]\frac{4z}{5} = \frac{4}{1} [/tex]

[tex]\frac{4z}{1} = \frac{20}{1} [/tex]

[tex]z = \frac{20}{4} [/tex]

⇒ z = 5

By substituting value of z into (1)

⇒ 4 (5) = x

⇒ x = 20

Thus the two numbers are 5 & 20 

Answer:

The required numbers are 5 and 20.

Step-by-step explanation:

Given : One number is four times another number.

Let the first number is 'x'

The reciprocal of the first number is [tex]\frac{1}{x}[/tex]

and another number is '4x'

The reciprocal of the another number is [tex]\frac{1}{4x}[/tex]

The sum of their reciprocals is [tex]\frac{1}{4}[/tex]

i.e. [tex]\frac{1}{x}+\frac{1}{4x}=\frac{1}{4}[/tex]

Solving the equation,

[tex]\frac{4+1}{4x}=\frac{1}{4}[/tex]

[tex]\frac{5}{4x}=\frac{1}{4}[/tex]

Cross multiply,

[tex]5\times 4=1\times 4x[/tex]

[tex]20=4x[/tex]

[tex]x=\frac{20}{4}[/tex]

[tex]x=5[/tex]

Another number is [tex]4x=5\times 4=20[/tex]

Therefore, the required numbers are 5 and 20.

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