Question 1045390: A number added to thrice its reciprocal is equal to 13/2. what is the number?
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52788)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! There is nothing that says that the number is a positive integer,
but if that had been meant,the fifth grader approach would work well.
Otherwise, we could use the algebra approach.
THE FIFTH GRADER APPROACH:
It cannot be a very small number, like  ,
because the sum would be too low.
It cannot be  or more,
because the sum would be more than  .
It must be a multiple of  ,
because the sum has a in the denominator.
Could the number be  ?
Its reciprocal is  , and the sum i
 .
That is not  .
The sum is less than  ,
and obviously the bigger the starting number,
the larger the sum will be,
so let's try  .
The reciprocal of is 1 ,
and the sum of plus thrice its reciprocal is
 .
So, the number is  .
THE ALGEBRA APPROACH:
 = the mystery number, and
 = its reciprocal, so we know that  .
Then,
 = the mystery number added to thrice its reciprocal.
The problem say that sum is , so our equation is
 .
Solving:
1
We multiply both sides of the equal sign in that equation times  .
Since we now that , we know we get an equivalent equation.
We can solve that equation by factoring,
by completing the square,
or by using the quadratic formula,
to get the solutions
 and  .
|
|
|
