Question 1200200
.
A bottle filled with varnish cost $1.10. if the varnish alone is worth $1.00 more 
than the bottle, find the value of the bottle.
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            This problem and many other similar problems is/are well known  " trap "  problem/problems.


           Those, who do not know that it is a trap,  usually fall in it,

            especially those of them who are in hurry to answer without thinking  (and without checking).


            The answer  $1.00  and  $0.10,  given by the other person,  is,  OBVIOUSLY,  incorrect

            (because the difference of  $1.00  and  $0.10  is not  $1.00).


            The correct answer is  $0.05  for the empty bottle and  $1.05  for the varnish alone.


            One way to get the correct answer is to get it mentally,  after thinking couple of seconds.


            Another way is to solve it formally,  as follows.



<pre>
x   dollars for varnish;

x-1 dollars for the bottle.


Total cost equation

    x + (x-1) = 1.10  dollars

    x + x = 1.10 + 1

     2x   =   2.10

      x   =   2.10/2 = 1.05,


giving the above mentioned correct answer.
</pre>

Solved, with complete explanations.



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You may ask me, regarding this and other similar trap problems - - - how to avoid falling in such trap, 

if you do not know about it in advance ?  &nbsp;&nbsp;Is there a way ?  &nbsp;&nbsp;Does it exist ?


The answer is: &nbsp;&nbsp;YES, &nbsp;the way does exist.


This way is to &nbsp;&nbsp;{{{highlight(highlight(CHECK))}}} &nbsp;&nbsp;your answer before you release it to outside.



By the way, &nbsp;checking is absolutely necessary step of each problem solution.

Without it, &nbsp;no one answer can be accepted.