document.write( "Question 855796: How many pounds of a 70% copper alloy must be melted with how many pounds of a 90% copper alloy to obtain 100 pounds of an 81% copper alloy? \n" ); document.write( "
Algebra.Com's Answer #515572 by josmiceli(19441)\"\" \"About 
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Let \"+a+\" = pounds of 70% alloy needed
\n" ); document.write( "Let \"+b+\" = pounds of 90% alloy needed
\n" ); document.write( "------------------------------------
\n" ); document.write( "(1) \"+a+%2B+b+=+100+\"
\n" ); document.write( "(2) \"+%28+.7a+%2B+.9b+%29+%2F+100+=+.81+\"
\n" ); document.write( "-------------------------------
\n" ); document.write( "(2) \"+.7a+%2B+.9b+=+81+\"
\n" ); document.write( "(2) \"+7a+%2B+9b+=+810+\"
\n" ); document.write( "----------------------
\n" ); document.write( "Multiply both sides of (1) by \"+7+\"
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) \"+7a+%2B+9b+=+810+\"
\n" ); document.write( "(1) \"+-7a+-+7b+=+-700+\"
\n" ); document.write( "\"+2b+=+110+\"
\n" ); document.write( "\"+b+=+55+\"
\n" ); document.write( "and
\n" ); document.write( "(1) \"+a+%2B+b+=+100+\"
\n" ); document.write( "\"+a+=+45+\"
\n" ); document.write( "-------------------
\n" ); document.write( "45 pounds of 70% alloy are needed
\n" ); document.write( "55 pounds of 90% alloy are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) \"+%28+.7%2A45+%2B+.9%2A55+%29+%2F+100+=+.81+\"
\n" ); document.write( "(2) \"+%28+31.5+%2B+49.5+%29+%2F+100+=+.81+\"
\n" ); document.write( "(2) \"+81+=+.81%2A100+\"
\n" ); document.write( "(2) \"+81+=+81+\"
\n" ); document.write( "OK\r
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