The sum of two natural numbers is 8. Determine the numbers if the sum of their…
2016
The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.
- A.
3,5
- B.
6,2
- C.
4,4
- D.
None of these
Attempted by 5 students.
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Correct answer: A
Let the two natural numbers be x and y.
We are given that x + y = 8 and the sum of their reciprocals is 1/x + 1/y = 8/15.
Combine the reciprocal terms: (x + y) / xy = 8/15.
Substitute the known sum x + y = 8 into the equation: 8 / xy = 8/15.
Solving for the product xy gives xy = 15.
Find two natural numbers that sum to 8 and multiply to 15. The factors of 15 are (1, 15) and (3, 5). Only the pair (3, 5) satisfies x + y = 8.
The two numbers are 3 and 5.