document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141777>Question 141777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam emptied his collection of nickels and dimes on his bed. If his 46 coins were worth $3.10, how many coins of each type did he have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103274 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=number of nickels<BR>\n" );
document.write( "And let y=number of dimes\r<BR>\n" );
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document.write( "Now we are told:\r<BR>\n" );
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document.write( "x+y=46-------------------------------------------eq1\r<BR>\n" );
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document.write( "and($ understood)<BR>\n" );
document.write( "0.05x+0.25y=3.10-------------------------------------eq2\r<BR>\n" );
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document.write( "Multiply eq1 by 0.05\r<BR>\n" );
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document.write( "0.05x+0.05y=2.3------------------------eq1a\r<BR>\n" );
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document.write( "Subtract eq1a from eq2\r<BR>\n" );
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document.write( "0.20y=0.80  divide both sides by 0.20<BR>\n" );
document.write( "y=4--------------------------------------number of quarters\r<BR>\n" );
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document.write( "Substitute y=4 into eq1<BR>\n" );
document.write( "x+4=46  subtract 4 from each side\r<BR>\n" );
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document.write( "x+4-4=46-4  collect like terms\r<BR>\n" );
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document.write( "x=42-----------------------------number of nickels\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "42+4=46<BR>\n" );
document.write( "46=46<BR>\n" );
document.write( "and<BR>\n" );
document.write( "4*0.25+42*0.05=3.10<BR>\n" );
document.write( "1.00+2.10=3.10<BR>\n" );
document.write( "3.10=3.10\r<BR>\n" );
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document.write( "Another way to solve this problem using 1 unknown:\r<BR>\n" );
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document.write( "Let x=number of nickels<BR>\n" );
document.write( "Then 46-x=number of quarters<BR>\n" );
document.write( "0.05x+0.25(46-x)=3.10   get rid of parens<BR>\n" );
document.write( "0.05x+11.50-0.25x=3.10  subtract 11.50 from each side\r<BR>\n" );
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document.write( "0.05x+11.50-11.50-0.25x=3.10-11.50  collect like terms\r<BR>\n" );
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document.write( "-0.20x=-8.40  divide both sides by -0.20<BR>\n" );
document.write( "x=42--------------------------------------------number of nickels\r<BR>\n" );
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document.write( "46-42=4--------------------------------------number of quarters\r<BR>\n" );
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document.write( "Hope this helps----ptaylor </SPAN>\n" );
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