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Question 135921: Where 3 times a certain number is added to twice its reciprocal the result is 5. What is the number
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=the certain number
3x=3 times the certain number
The reciprocal of the certain number is 1/x
Twice the reciprocal is 2/x
Now we are told that:
3x+(2/x)=5 multiply each term by x
3x^2+2=5x subtract 5x from each side
3x^2-5x+2=0--------quadratic in standard form and it can be factored
(3x-2)(x-1)=0
3x-2=0
x=2/3
and
x-1=0
x=1
CK
3*(2/3)=2;
twice the reciprocal of 2/3 is 6/2 or 3
and 3+2=5 ok
Now
3*1=3
twice the reciprocal of 1 is 2
and 3+2=5 ok
SO, BOTH ANSWERS ARE GOOD!!
Hope this helps---ptaylor
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