SOLUTION: The sum of an integer and its reciprocal is 65/8. Find the integer.

Question 288941: The sum of an integer and its reciprocal is 65/8. Find the integer.
Found 2 solutions by Alan3354, unlockmath:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
It's 8
There's a clue in the denominator.

Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Let's have "x" be the integer so we can set up the following equation as:
x+1/x=65/8 Now multiply both sides by 8x to get:
8x^2+8=65x Subtract 65x from both sides to get:
8x^2-65x+8=0 Solve for x to get:
(8x-1)(x-8)=0
x=1/8
x=8
Since we want an integer the answer will be:
8 (you can check this answer in the original equation)
Make sense?
RJ
Check out a book I wrote at:
www.math-unlock.com

RELATED QUESTIONS
solving integer problems the sum of an integer and its reciprocal is 68/8. find the... (answered by ewatrrr,Fombitz)
typo in the last one its actually the sume of an integer and its reciprocal is 65/8.... (answered by Fombitz,ewatrrr)
the sum of an integer and its reciprocal is 145/12. what is the integer. (answered by Alan3354)
The sum of the integer and twice its reciprocal is 11/3. Find the... (answered by ichudov)
The sum of an integer and its reciprocal is 82/9. Find the integer. Could you please... (answered by checkley77)
Five minus twice the reciprocal of an integer is 39/8. Find the... (answered by MathLover1)
The sum of twice a positive integer and 4 times the reciprocal of the integer is 9. Find... (answered by nyc_function)
The sum of an integer and its square is 12. Find the... (answered by ptaylor)
The sum of an integer and its square is 42. Find the... (answered by checkley71)