Class 10 Exam > Class 10 Questions > The sum of two numbers is 8 and the sum of th...
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The sum of two numbers is 8 and the sum of their reciprocals is 8/15. Find the numbers.
- a)5, 3
- b)7, 1
- c)4, 4
- d)2, 6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The sum of two numbers is 8 and the sum of their reciprocals is 8/15.F...
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that the two numbers are x and y.
Given:
1) The sum of two numbers is 8:
x + y = 8
2) The sum of their reciprocals is 8/15:
1/x + 1/y = 8/15
We can solve this system of equations to find the values of x and y.
Solving the System of Equations:
To solve this system of equations, we can use the method of substitution.
1) Solve the first equation for one variable in terms of the other. Let's solve for y in terms of x:
y = 8 - x
2) Substitute this value of y in the second equation:
1/x + 1/(8 - x) = 8/15
3) Multiply through by 15x(8 - x) to eliminate fractions:
15(8 - x) + 15x = 8x(8 - x)
4) Simplify and rearrange the equation:
120 - 15x + 15x = 64x - 8x^2
120 = 64x - 8x^2
5) Rewrite the equation in standard form:
8x^2 - 64x + 120 = 0
6) Factor the quadratic equation:
4(x^2 - 8x + 15) = 0
4(x - 3)(x - 5) = 0
From this equation, we can see that the possible values for x are 3 and 5.
7) Substitute each value of x back into the first equation to find the corresponding value of y:
For x = 3:
y = 8 - 3
y = 5
For x = 5:
y = 8 - 5
y = 3
Therefore, the numbers are 3 and 5, which corresponds to option A: 5, 3.
Let's assume that the two numbers are x and y.
Given:
1) The sum of two numbers is 8:
x + y = 8
2) The sum of their reciprocals is 8/15:
1/x + 1/y = 8/15
We can solve this system of equations to find the values of x and y.
Solving the System of Equations:
To solve this system of equations, we can use the method of substitution.
1) Solve the first equation for one variable in terms of the other. Let's solve for y in terms of x:
y = 8 - x
2) Substitute this value of y in the second equation:
1/x + 1/(8 - x) = 8/15
3) Multiply through by 15x(8 - x) to eliminate fractions:
15(8 - x) + 15x = 8x(8 - x)
4) Simplify and rearrange the equation:
120 - 15x + 15x = 64x - 8x^2
120 = 64x - 8x^2
5) Rewrite the equation in standard form:
8x^2 - 64x + 120 = 0
6) Factor the quadratic equation:
4(x^2 - 8x + 15) = 0
4(x - 3)(x - 5) = 0
From this equation, we can see that the possible values for x are 3 and 5.
7) Substitute each value of x back into the first equation to find the corresponding value of y:
For x = 3:
y = 8 - 3
y = 5
For x = 5:
y = 8 - 5
y = 3
Therefore, the numbers are 3 and 5, which corresponds to option A: 5, 3.
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Community Answer
The sum of two numbers is 8 and the sum of their reciprocals is 8/15.F...
Let the two numbers be x and y.
According to the given conditions, x + y = 8...(1)
and
...(2)
Putting value of x = 8 – y in (2), we get
⇒ y2 – 8y + 15 = 0 ⇒ y2 – 5y – 3y + 15 = 0
⇒ (y – 5) (y – 3) = 0 ⇒ y = 5 or y = 3
From (1), x = 3 or x = 5
Thus, the numbers are 5 and 3.
According to the given conditions, x + y = 8...(1)
and
...(2)Putting value of x = 8 – y in (2), we get
⇒ y2 – 8y + 15 = 0 ⇒ y2 – 5y – 3y + 15 = 0
⇒ (y – 5) (y – 3) = 0 ⇒ y = 5 or y = 3
From (1), x = 3 or x = 5
Thus, the numbers are 5 and 3.
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The sum of two numbers is 8 and the sum of their reciprocals is 8/15.Find the numbers.a)5, 3b)7, 1c)4, 4d)2, 6Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The sum of two numbers is 8 and the sum of their reciprocals is 8/15.Find the numbers.a)5, 3b)7, 1c)4, 4d)2, 6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of two numbers is 8 and the sum of their reciprocals is 8/15.Find the numbers.a)5, 3b)7, 1c)4, 4d)2, 6Correct answer is option 'A'. Can you explain this answer?.
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