document.write( "Question 669328: Hometown hardware stocks quarts of flat wall paint. The quarts cost 5.25 and gallons cost 16.87. If they have 27 more quarts than gallons and if their inventory is worth 2198.91, how much of each size do they have on hand? \n" ); document.write( "

Algebra.Com's Answer #416375 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of quarts they have
\n" ); document.write( "Let $\"+b+\"$ = number of gallons they have
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+=+b+%2B+27+\"$
\n" ); document.write( "(2) $\"+5.25a+%2B+16.87b+=+2198.91+\"$
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) $\"+525a+%2B+1687b+=+219891+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+-+b+=+27+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Multiply both sides of (1) by $\"+1687+\"$
\n" ); document.write( "and add the equations
\n" ); document.write( "(2) $\"+525a+%2B+1687b+=+219891+\"$
\n" ); document.write( "(1) $\"+1687a+-+1687b+=+45549+\"$
\n" ); document.write( " $\"+2212a+=+265440+\"$
\n" ); document.write( " $\"+a+=+120+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+=+b+%2B+27+\"$
\n" ); document.write( "(1) $\"+b+=+a+-+27+\"$
\n" ); document.write( "(1) $\"+b+=+120+-+27+\"$
\n" ); document.write( "(1) $\"+b+=+93+\"$
\n" ); document.write( "120 is the number of quarts they have
\n" ); document.write( "93 is the number of gallons they have
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+5.25%2A120+%2B+16.87%2A93+=+2198.91+\"$
\n" ); document.write( "(2) $\"+630+%2B+1568.91+=+2198.91+\"$
\n" ); document.write( "(2) $\"+2198.91+=+2198.91+\"$
\n" ); document.write( "OK\r
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