SOLUTION: The sum of the reciprocals of two consecutive integers is 9/20. Find the two integers.
Algebra.Com
Question 632103: The sum of the reciprocals of two consecutive integers is 9/20. Find the two integers.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE FIFTH GRADER WAY:
The reciprocals are fractions that have those two integers for denominators.
To add them, we can use the product of those two integers as the common denominator.
We know two numbers that are consecutive integers and whose product is 20.
They are 4 and 5.
Let's see if they work.
The numbers are and .
THE ALGEBRA WAY:
Let the two consecutive numbers be and .
Their reciprocals are
and
The sum of those reciprocals is
We are told that the sum is , so
is our equation.
Multiplying both sides times , or "equating the cross products", we get
We transform that into the standard form of a quadratic equation.
--> --> -->
Since we expect at least one integer solution for , factoring should work to solve the equation.
If we are not good at factoring, we solve using the quadratic formula.
If we are good at factoring, we factor to find that
We write the equation as
and realize that the solutions to that equation are
and
We discard the solution that is not an integer, and find that the two integers are
and .
RELATED QUESTIONS
The sum of the reciprocals of two consecutive integers is 7/12. Find the two... (answered by Fombitz)
the sum of the reciprocals of two consecutive integers is 11/30. find the two... (answered by stanbon)
the sum of the reciprocals of two consecutive integers is 7/12. find the two... (answered by richwmiller,MathLover1)
the sum of the reciprocals of two consecutive odd integers is 20/99. find the two... (answered by Alan3354)
The sum of the reciprocals of two consecutive odd integers is 20/90. Find the two... (answered by edjones)
The sum of the reciprocals of two consecutive odd integers is 20/99. Find the two... (answered by palanisamy,edjones)
The sum of the reciprocals of two consecutive integers is 5/6. Find two... (answered by Fombitz)
The sum of the reciprocals of two consecutive even integers is 11/60. Find the... (answered by funmath)
The sum of the reciprocals of two consecutive even integers is 11/60. Find the... (answered by ankor@dixie-net.com)