A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/8. Find the two integer

Question

SCORPION-xisa [38]

3 years ago

11

A positive integer is twice another. The difference of the reciprocals of the two positive integers is 1/8. Find the two integer

s.

Mathematics

2 answers:

igomit [66] · Answer 1 · 2022-06-21T16:40:36+03:00

To solve this problem you must apply the proccedure shown below:
1. You have:
x: the positive integer that is twice another.
y: the other positive integer.
2. Therefore, you must write a system of equations, as following:
x=2y
(1/y)-/(1/x)=1/8
3. By susbtitution, you obtain:
(1/y)-/(1/2y)=1/8
y=4
x=2x4
x=8
The answer is: 8 and 4.

Wewaii [24] · Answer 2 · 2022-06-21T17:48:35+03:00

The two integers are $\boxed{\bf 4\text{ and }8}$ .

Further explanation:

Given:

Condition 1: The first integer is the twice to the other integer.

Condition 2:The differences of the reciprocal of the two positive integers is $\frac{1}{8}$ .

Calculation:

Consider the first positive integer as $x$ and the second positive integer as $y$ .

Apply the first condition to find the first equation:

$\boxed{x=2y}$ …… (1)

Apply the second condition to find the second equation:

$\boxed{\dfrac{1}{y}-\dfrac{1}{x}=\dfrac{1}{8}}$ …… (2)

There are two equations and the two unknown it can be easily solved by the substitution method.

The substitution method is defined as the method in which first express one variable in the form of second variable and then substitute in the other equation to obtain the value of variable.

Substitute $2y$ for $x$ in equation (2) to obtain the value of $y$ .

$\begin{aligned}\dfrac{1}{y}-\dfrac{1}{{2y}}&=\dfrac{1}{8}\\ \frac{{2 - 1}}{{2y}}&=\dfrac{1}{8}\\ 2y&=8\\ y&=4\end{aligned}$