A number minus 12 times its reciprocal is equal to 1. Find the number.

Question

Hi, I really do not get this question. Every time I try to solve this I get x-12 = x, which can't be right. If someone could please explain what I'm doing wrong and how to do the problem right that would be great :) 

Answer 1

Amber/Linda,

 

It looks to me that what is being asked is

 

x - 12*1/(x) = 1

 

or

x^2 -x -12 = 0

x^2 - 4x + 3x -12 = 0

x(x-4) +3(x-4) = 0

(x-4)(x+3) = 0

 

x = 4 and x = -3

 

Answer 2

Hmmm, weird question.  Yes, if you are starting with (x-12)*(1/x)=1, you get your contradiction.  

 

Perhaps they mean (x-12)*(1/(x-12))=1, which would be true for all numbers except 12?  Can anyone else see another way to read these words?