document.write( "Question 270008: There was a farmer who was selected after a deal. A tax payer said return $100 for exactly 100 animals. He went to buy the animals. He was going to waste exactly $100 for exactly 100 animals. Sheep costs $.5, cows cost $1, and horse costs $10. Name three possibilities for this problem. \n" ); document.write( "

Algebra.Com's Answer #197851 by josmiceli(19441) $\"\"$ $\"About$

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Which combination of $\"100\"$ animals cost $100?
\n" ); document.write( "Let $\"s\"$ = number of sheep he bought
\n" ); document.write( "Let $\"c\"$ = number of cows he bought
\n" ); document.write( "Let $\"h\"$ = number of horses he bought
\n" ); document.write( " $\"50s+%2B+100c+%2B+1000h+=+10000\"$ (in cents)
\n" ); document.write( " $\"5s+%2B+10c+%2B+100h+=+1000\"$
\n" ); document.write( "(1) $\"s+%2B+2c+%2B+20h+=+200\"$
\n" ); document.write( "He buys $\"100\"$ animals, so
\n" ); document.write( "(2) $\"s+%2B+c+%2B+h+=+100\"$
\n" ); document.write( "This is 3 unknowns and only 2 equations, so it's
\n" ); document.write( "not directly solvable, but a little work will give
\n" ); document.write( "some answers
\n" ); document.write( "--------------------------------------------------
\n" ); document.write( "If I subtract (2) from (1):
\n" ); document.write( "(1) $\"s+%2B+2c+%2B+20h+=+200\"$
\n" ); document.write( "(2) $\"-s+-+c+-+h+=+-100\"$
\n" ); document.write( " $\"c+%2B+19h+=+100\"$
\n" ); document.write( "According to this, he could buy $\"5\"$ horses
\n" ); document.write( "and $\"5\"$ cows
\n" ); document.write( " $\"5+%2B+19%2A5+=+100\"$
\n" ); document.write( "Then, using (2),
\n" ); document.write( "(2) $\"s+%2B+c+%2B+h+=+100\"$
\n" ); document.write( " $\"s+%2B+5+%2B+5+=+100\"$
\n" ); document.write( " $\"s+=+90\"$
\n" ); document.write( "---------------------------------------------------------------
\n" ); document.write( "he could buy $\"5\"$ horses, $\"5\"$ cows, and $\"90\"$ sheep
\n" ); document.write( "---------------------------------------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"s+%2B+2c+%2B+20h+=+200\"$
\n" ); document.write( " $\"90+%2B+2%2A5+%2B+20%2A5+=+200\"$
\n" ); document.write( " $\"90+%2B+10+%2B+100+=+200\"$
\n" ); document.write( " $\"200+=+200\"$
\n" ); document.write( "OK
\n" ); document.write( "---------------------------
\n" ); document.write( "Go back to $\"c+%2B+19h+=+100\"$
\n" ); document.write( "Suppose he bought $\"4\"$ horses?
\n" ); document.write( " $\"c+%2B+19%2A4+=+100\"$
\n" ); document.write( " $\"c+=+100+-+76\"$
\n" ); document.write( " $\"c+=+24\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"s+%2B+c+%2B+h+=+100\"$
\n" ); document.write( " $\"s+%2B+24+%2B+4+=+100\"$
\n" ); document.write( " $\"s+=+100+-+28\"$
\n" ); document.write( " $\"s+=+72\"$
\n" ); document.write( "---------------------------------------------------------------
\n" ); document.write( "he could buy $\"4\"$ horses, $\"24\"$ cows, and $\"72\"$ sheep
\n" ); document.write( "---------------------------------------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"s+%2B+2c+%2B+20h+=+200\"$
\n" ); document.write( " $\"72+%2B+2%2A24+%2B+20%2A4+=+200\"$
\n" ); document.write( " $\"72+%2B+48+%2B+80+=+200\"$
\n" ); document.write( " $\"200+=+200\"$
\n" ); document.write( "OK
\n" ); document.write( "----------------------------
\n" ); document.write( "Suppose he bought $\"3\"$ horses?
\n" ); document.write( " $\"c+%2B+19%2A3+=+100\"$
\n" ); document.write( " $\"c+=+100+-+57\"$
\n" ); document.write( " $\"c+=+43\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"s+%2B+c+%2B+h+=+100\"$
\n" ); document.write( " $\"s+%2B+43+%2B+3+=+100\"$
\n" ); document.write( " $\"s+=+100+-+46\"$
\n" ); document.write( " $\"s+=+54\"$
\n" ); document.write( "---------------------------------------------------------------
\n" ); document.write( "he could buy $\"3\"$ horses, $\"43\"$ cows, and $\"54\"$ sheep
\n" ); document.write( "---------------------------------------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"s+%2B+2c+%2B+20h+=+200\"$
\n" ); document.write( " $\"54+%2B+2%2A43+%2B+20%2A3+=+200\"$
\n" ); document.write( " $\"54+%2B+86+%2B+60+=+200\"$
\n" ); document.write( " $\"200+=+200\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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