document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108895>Question 1108895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Set up a system of linear equations and solve for the indicated quantities.\r<BR>\n" );
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document.write( "Nathan buys a combination of 45 cents stamps and 65 cents stamps at the post office. If he spends exactly $24.50 on 50 stamps, how many of each type did he buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723969 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Nathan buys a combination of 45 cents stamps and 65 cents stamps at the post office. If he spends exactly $24.50 on 50 stamps, how many of each type did he buy? \r<BR>\n" );
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document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+ ALIGN=MIDDLE  ALT=\"45+\"   DISABLED_style= \"max-width:90%; height:auto;\" >cents  stamps be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65 ALIGN=MIDDLE  ALT=\"65\"   DISABLED_style= \"max-width:90%; height:auto;\" > cents stamps <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "first convert cents to dollars:  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+ ALIGN=MIDDLE  ALT=\"45+\"   DISABLED_style= \"max-width:90%; height:auto;\" >cents = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.45+ ALIGN=MIDDLE  ALT=\"0.45+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+ ALIGN=MIDDLE  ALT=\"65+\"   DISABLED_style= \"max-width:90%; height:auto;\" >cents = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.65+ ALIGN=MIDDLE  ALT=\"0.65+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "if Nathan buys  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps , we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1\r<BR>\n" );
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document.write( "If he spends exactly $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.50 ALIGN=MIDDLE  ALT=\"24.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > on all stamps, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.45x%2B0.65y=24.50 ALIGN=MIDDLE  ALT=\"0.45x%2B0.65y=24.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2\r<BR>\n" );
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document.write( "solve the system:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.45x%2B0.65y=24.50 ALIGN=MIDDLE  ALT=\"0.45x%2B0.65y=24.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2<BR>\n" );
document.write( "----------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1 ...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50-y ALIGN=MIDDLE  ALT=\"x=50-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1a...substitute in eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.45%2850-y%29%2B0.65y=24.50 ALIGN=MIDDLE  ALT=\"0.45%2850-y%29%2B0.65y=24.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2..solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.5-0.45y%2B0.65y=24.50 ALIGN=MIDDLE  ALT=\"22.5-0.45y%2B0.65y=24.50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2y=24.50-22.5 ALIGN=MIDDLE  ALT=\"0.2y=24.50-22.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2y=2 ALIGN=MIDDLE  ALT=\"0.2y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2F0.2 ALIGN=MIDDLE  ALT=\"y=2%2F0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10 ALIGN=MIDDLE  ALT=\"y=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now go back to eq.1a and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50-y ALIGN=MIDDLE  ALT=\"x=50-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.1a\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=50-10 ALIGN=MIDDLE  ALT=\"x=50-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40 ALIGN=MIDDLE  ALT=\"x=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Nathan did buy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45+ ALIGN=MIDDLE  ALT=\"45+\"   DISABLED_style= \"max-width:90%; height:auto;\" >cents  stamps, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+ ALIGN=MIDDLE  ALT=\"65+\"   DISABLED_style= \"max-width:90%; height:auto;\" >cents  stamps\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );