document.write( "Question 178568: A merchant blends tea that sells for $3.45 a pound with tea that sells for $2.15 a pound to produce 80 pounds of a mixture that sells for $2.75 a pound.
\n" ); document.write( "How many pounds of the $3.45/lbs of tea does the new mixture contain? And how many pounds of the $2.15/lbs of tea does the new mixture contain? \n" ); document.write( "
Algebra.Com's Answer #133543 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"a\"= the pounds of the more expensive tea needed
\n" ); document.write( "Let \"b\"= the pounds of the less expensive tea needed
\n" ); document.write( "given:
\n" ); document.write( "(1) \"a+%2B+b+=+80\"
\n" ); document.write( "(2) \"345a+%2B+215b+=+80%2A275\" (in cents)
\n" ); document.write( "--------------------------
\n" ); document.write( "In words, (2) says
\n" ); document.write( "(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =
\n" ); document.write( "(lbs of mixture x price/lb of mixture)
\n" ); document.write( "--------
\n" ); document.write( "Multiply both sides of (1) by \"215\" and then
\n" ); document.write( "subtract from (2)
\n" ); document.write( "\"345a+%2B+215b+=+80%2A275\"
\n" ); document.write( "\"-215a+-+215b+=+-80%2A215\"
\n" ); document.write( "\"130a+=+80%2A60\"
\n" ); document.write( "\"130a+=+4800\"
\n" ); document.write( "\"a+=+36.92\"
\n" ); document.write( "and, from (1)
\n" ); document.write( "(1) \"a+%2B+b+=+80\"
\n" ); document.write( "\"36.92+%2B+b+=+80\"
\n" ); document.write( "\"b+=+80+-+36.92\"
\n" ); document.write( "\"b+=+43.08\"
\n" ); document.write( "36.92 lbs of the $3.45 tea and 43.08 lbs of the $2.15 tea are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) \"345a+%2B+215b+=+80%2A275\"
\n" ); document.write( "(2) \"345%2A36.92+%2B+215%2A43.08+=+80%2A275\"
\n" ); document.write( "\"12740+%2B+9260+=+22000\"
\n" ); document.write( "\"22000+=+22000\"
\n" ); document.write( "OK \n" ); document.write( "
\n" );