Question 543816
<pre>
The easy answer is for him to buy 100 sheep for $1000.

But the answer you want is

 19 cows    × $50.00 =  $950.00
  1 sheep   × $10.00 =    10.00
 80 rabbits × $  .50 =    40.00
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100 animals          = $1000.00

I got the answer using number theory.  Are you studying
number theory?  That's a university mathematics course.
If so, let me know in the thank-you note and I'll show you
how to solve it using number theory, in the
topic of linear Diophantine equations.

Edwin</pre>