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One number is four times another number. The sum of their reciprocals is 1/4 . What is the answer

User Jakoss
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2 Answers

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


4 z = x ... (1)


(1)/(z) + (1)/(x) ... (2)

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


(1)/(z) + (1)/(4z) = (1)/(4)


(5)/(4z) = (1)/(4)

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


(4z)/(5) = (4)/(1)


(4z)/(1) = (20)/(1)


z = (20)/(4)

⇒ z = 5

By substituting value of z into (1)

⇒ 4 (5) = x

⇒ x = 20

Thus the two numbers are 5 & 20



User Faysal Ahmet
by
8.5k points
0 votes

Answer:

The required numbers are 5 and 20.

Explanation:

Given : One number is four times another number.

Let the first number is 'x'

The reciprocal of the first number is
(1)/(x)

and another number is '4x'

The reciprocal of the another number is
(1)/(4x)

The sum of their reciprocals is
(1)/(4)

i.e.
(1)/(x)+(1)/(4x)=(1)/(4)

Solving the equation,


(4+1)/(4x)=(1)/(4)


(5)/(4x)=(1)/(4)

Cross multiply,


5* 4=1* 4x


20=4x


x=(20)/(4)


x=5

Another number is
4x=5* 4=20

Therefore, the required numbers are 5 and 20.

User Apatsekin
by
7.1k points

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