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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.
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.
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 ? Is there a way ? Does it exist ?
The answer is: YES, the way does exist.
This way is to your answer before you release it to outside.
By the way, checking is absolutely necessary step of each problem solution.
Without it, no one answer can be accepted.