SOLUTION: The sum of a positive number and 13 is 140 times the reciprocal of the number. Find the number

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Question 984049: The sum of a positive number and 13 is 140 times the reciprocal of the number. Find the number
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's a positive number be x and its reciprocal 1%2Fx
given:
x%2B13=140%281%2Fx%29 ....solve for x
x%2B13=140%2Fx
%28x%2B13%29x=140
x%5E2%2B13x=140
x%5E2%2B13x-140=0...factor completely
x%5E2-7x%2B20x-140=0
%28x%5E2-7x%29%2B%2820x-140%29=0
x%28x-7%29%2B20%28x-7%29=0
%28x-7%29%28x%2B20%29+=+0
solutions:
if %28x-7%29+=+0=>highlight%28x=7%29
if %28x%2B20%29+=+0=>highlight%28x=-20%29

check:
x%2B13=140%281%2Fx%29...if x=7
7%2B13=140%281%2F7%29
20=140%2F7
20=20........true
x%2B13=140%281%2Fx%29...if x=-20
-20%2B13=140%281%2F-20%29
-7=-140%2F20
-7=-7........true