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The sum of two numbers is 8 and the sum of their reciprocals is 8/15 . Find the numbers.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
To find: The two numbers whose sum is 8 and sum of their reciprocals is 8/15.
Let the first number be x and the second number be y.
According to the question statement:
x + y = 8 (equation 1)
1/x + 1/y = 8/15 (equation 2)
From equation 1, we will get the value of x.
x + y = 8
x = 8 – y (equation 3)
Now on simplifying equation 2, we will get
1/x + 1/y = 8/15
(x + y)/xy = 8/15 (equation 4)
Put the value of equation 3 in equation 4.
[(8-y) + y] / (8 – y)y = 8/15
[8 – y + y] / (8y – y2) = 8/15
8/(8y – y2) = 8/15
1/(8y – y2) = 1/15
8y – y2 = 15
y2 – 8y + 15 = 0
y2 – (5+3)y + 15 = 0
y2 – 5y – 3y + 15 = 0
y (y – 5) – 3 (y – 5) = 0
(y – 3) (y – 5) = 0
So, y = 3 or 5
Now, we know that the sum of two numbers that are x and y is 8.
We have found the value of ‘y’ = 3
So, the value of ‘x’ will be = 5.
Hence, 3 and 5 are the two numbers whose sum is 8 and the sum of their reciprocals is 8/15.
Table of content
Two Numbers whose Sum is 8 and Sum of their Reciprocals is 8/15
The two numbers whose sum is 8 and the sum of their reciprocals is 8/15 are 3 and 5. The result or solution after adding two or more numbers or terms is known as the sum. The sum is a method of putting things together as a result. To put it another way, adding two or more numbers together results in a new total called sum.
Example of sum: 3 + 5 = 8
In the given example, 3 and 5 have been added to get their sum which is 8.
The concept of sum is used in our daily life whenever we calculate anything like in calculating the groceries total, monthly expense, etc.
Summary:
The sum of two numbers is 8 and the sum of their reciprocals is 8/15. Find the numbers.
The two numbers for which the sum is 8 and the sum of their reciprocals is 8/15 are 3 and 5. It can be easily determined by assuming that the first number is x and the second number is y. After that form the equation based on the question statement and solve it to get the answer.
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