SOLUTION: a hippo weighs 2000 pounds more than half of its weight, How much does the hippo weigh?

That's trick wording and if you get tricked by it, it will be because you
forgot to consider the fact that that the only thing you can add one-half of to
and get the whole thing is the other half of that thing.  And since one half is
2000, the other half must be 2000 also and so the whole is twice 2000 or 4000.

Suppose the problem had read:

A hippo weighs 2000 pounds more than THE OTHER half of its weight, How much
does the hippo weigh?

Then you'd immediately answer 4000 pounds, right?

Everything is one half of itself more than the other half of itself!  And
conversely, the only thing something could be more than one half of itself is
the other half of itself.  So what's 2000 lbs. half of?  Andwer: 4000 lbs.  
    
But for those who can't reason the above out for themselves, :-), we must
use algebra:



Clear of fractions by multiplying through every term by 2 





Subtract w from both sides:



When we are learning algebra sometimes we can just reason out the answer to a
word problem without doing any algebra, as in this case.  Then we ask "Why
should we be made to do something by a longer method (algebra) when we could
have done it a shorter way, maybe even in our heads? (as this one).  Good
question, and the answer is 3-fold.  Making you do that gives you practice of
principles that you need to know when solving harder problems when the answer
is not obvious like this one is. Secondly you aren't bogged down by having to
do more complicated reasoning while you're learning the principle.  It would be
hard to learn the principles using only examples of problems too hard to solve
by easier methods, for then you'd be distracted from learning the principles by
the complexity of the problem.  Thirdly, it's easy to check your answer to such
problems and know you'de doing it correctly (or incorrectly).

Edwin