SOLUTION: Good day Sir/Madam, please help me with this word problem. Your help means a lot. The sum of the reciprocals of two consecutive integers is 25/56. Find the integers. Thank

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Good day Sir/Madam, please help me with this word problem. Your help means a lot. The sum of the reciprocals of two consecutive integers is 25/56. Find the integers. Thank       Log On


   

Question 683680: Good day Sir/Madam, please help me with this word problem. Your help means a lot.
The sum of the reciprocals of two consecutive integers is 25/56. Find the integers.
Thank you very much!
Answer by Edwin Parker(36) About Me  (Show Source):
You can put this solution on YOUR website!
There is a typo, for there are no such consecutive integers.  I am guessing
that the 25/56 should have been 15/56.  I will assume that.

Smaller integer = x
Larger integer = x+1

                   1%2Fx%22%22%2B%22%221%2F%28x%2B1%29%22%22=%22%2215%2F56

Multiply through by LCD of 56x(x+1), written as expr%2856x%28x%2B1%29%2F1%29%2A%22%22

       expr%2856x%28x%2B1%29%2F1%29%2A%22%221%2Fx%22%22%2B%22%22expr%2856x%28x%2B1%29%2F1%29%2A%22%221%2F%0D%0A%0D%0A%0D%0A+++++++%28x%2B1%29%22%22=%22%22expr%2856x%28x%2B1%29%2F1%29%2A%22%2215%2F56

     expr%2856cross%28x%29%28x%2B1%29%2F1%29%2A%22%221%2Fcross%28x%29%22%22%2B%22%22expr%2856x%28cross%28x%2B1%29%29%2F1%29%2A%22%221%2F%28cross%28x%2B1%29%29%22%22=%22%22expr%28cross%2856%29x%28x%2B1%29%2F1%29%2A%22%2215%2Fcross%2856%29
   
             56(x+1) + 56x = 15x(x+1)

            56x + 56 + 56x = 15x² + 15x

                 112x + 56 = 15x² + 15x
                         0 = 15x² - 97x - 56
                         0 = (x - 7)(15x + 8)
             
                       x - 7 = 0;   15x + 8 = 0
                           x = 7        15x = -8
                                          x = -8%2F15

Ignore the fraction answer.

Thus the integers are x = 7 and x+1 = 8

Edwin