document.write( "Question 521522: There are 96 ducks and goats. There are 316 legs between the ducks and goats. How many of each are there? _______ Ducks ______ Goats \n" ); document.write( "

Algebra.Com's Answer #346506 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"d\"$ = number of ducks
\n" ); document.write( "Let $\"g\"$ = number of goats
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+d+%2B+g+=+96+\"$
\n" ); document.write( "(2) $\"+2d+%2B+4g+=+316+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+2d+%2B+4g+=+316+\"$
\n" ); document.write( "(1) $\"+-2d+-+2g+=+192+\"$
\n" ); document.write( " $\"+2g+=+124+\"$
\n" ); document.write( " $\"+g+=+62+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+d+%2B+g+=+96+\"$
\n" ); document.write( "(1) $\"+d+%2B+62+=+96+\"$
\n" ); document.write( "(1) $\"+d+=+34+\"$
\n" ); document.write( "There are 34 ducks and 62 goats
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+2d+%2B+4g+=+316+\"$
\n" ); document.write( "(2) $\"+2%2A34+%2B+4%2A62+=+316+\"$
\n" ); document.write( "(2) $\"+68+%2B+248+=+316+\"$
\n" ); document.write( "(2) $\"+316+=+316+\"$
\n" ); document.write( "OK \n" ); document.write( "

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