SOLUTION: What is "the sum of the reciprocal of a number and the reciprocal of 7 less than the number is 9 times the reciprocal of the original number...find the orginal number."

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: What is "the sum of the reciprocal of a number and the reciprocal of 7 less than the number is 9 times the reciprocal of the original number...find the orginal number."      Log On


   

Question 412280: What is "the sum of the reciprocal of a number and the reciprocal of 7 less than the number is 9 times the reciprocal of the original number...find the orginal number."
Answer by BadLandsBarn(8) About Me  (Show Source):
You can put this solution on YOUR website!
I am not sure if I understood how you set this up, I did:
N - (1/N + 1/7) = 9/N
N^2 -1 N/7 = 9

7N^2 + N -70 = 0
From here I used the quadratic equation.
N = (-1 +, - sqrt(1 - 4(7)(-70))/14
= -1 +, - sqrt(1 + 1960) / 14
(-1 + 44.28)/ 14
(-1 - 44.28)/ 14
N = 3.09, N =-3.23
Check
(3.09)^2 -1 + (3.09/7) = 9
9.5481 - 1 + .4414 = 8.9895