The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is
15
8
.
- A1, 7
- B4, 4
- C2, 6
- D3, 5
Solution & Step-by-step Explanation
Let the two natural numbers be x and y.
From the given conditions:
x+y=8
x
1
+
y
1
=
15
8
Simplifying the reciprocal equation:
xy
x+y
=
15
8
Substitute x+y=8 into the equation:
xy
8
=
15
8
⟹xy=15
We need two numbers whose sum is 8 and product is 15. We can form a quadratic equation or solve this by inspection:
The factors of 15 that add up to 8 are 3 and 5 (3×5=15 and 3+5=8).
Thus, the numbers are 3 and 5.
From the given conditions:
x+y=8
x
1
+
y
1
=
15
8
Simplifying the reciprocal equation:
xy
x+y
=
15
8
Substitute x+y=8 into the equation:
xy
8
=
15
8
⟹xy=15
We need two numbers whose sum is 8 and product is 15. We can form a quadratic equation or solve this by inspection:
The factors of 15 that add up to 8 are 3 and 5 (3×5=15 and 3+5=8).
Thus, the numbers are 3 and 5.