document.write( "Question 415232: Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are needed to make 50 gallons of the mixture? \n" ); document.write( "

Algebra.Com's Answer #291144 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = gallons of $6 syrup needed
\n" ); document.write( "Let $\"b\"$ = gallons of $.80 syrup needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+50\"$
\n" ); document.write( "(2) $\"%286a+%2B+.8b%29%2F50+=+2.36\"$
\n" ); document.write( "----------------------
\n" ); document.write( "(2) $\"6a+%2B+.8b+=+118\"$
\n" ); document.write( "(2) $\"60a+%2B+8b+=+1180\"$
\n" ); document.write( "Multiply both sides of (1) by $\"8\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"60a+%2B+8b+=+1180\"$
\n" ); document.write( "(1) $\"-8a+-+8b+=+-400\"$
\n" ); document.write( " $\"52a+=+780\"$
\n" ); document.write( " $\"a+=+15\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"a+%2B+b+=+50\"$
\n" ); document.write( " $\"15+%2B+b+=+50\"$
\n" ); document.write( " $\"b+=+35\"$
\n" ); document.write( "15 gallons of $6 syrup are needed
\n" ); document.write( "35 gallons of $.80 syrup are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"%286a+%2B+.8b%29%2F50+=+2.36\"$
\n" ); document.write( "(2) $\"%286%2A15+%2B+.8%2A35%29%2F50+=+2.36\"$
\n" ); document.write( " $\"+%2890+%2B+28%29%2F50+=+2.36\"$
\n" ); document.write( " $\"+118%2F50+=+2.36\"$
\n" ); document.write( " $\"118+=+118\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );