document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138996>Question 138996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a stack of books 81 cm high, we have a total of 21 books. there are 5 cm thick and others of 3 cm thick. how do we each thickness? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101372 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Number of thick books: x<BR>\n" );
document.write( "Number of thin books: y\r<BR>\n" );
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document.write( "Total number of books: 21, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=21 ALIGN=MIDDLE  ALT=\"x%2By=21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The total thickness of all of the thick books is 5x, because each of the x thick books accounts for 5 cm.\r<BR>\n" );
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document.write( "The total thickness of all of the thin books is 3y.\r<BR>\n" );
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document.write( "Together, the books make a stack that is 81 cm tall, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y=81 ALIGN=MIDDLE  ALT=\"5x%2B3y=81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply the first equation by -3:<BR>\n" );
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document.write( "Now notice that the coefficients on the y terms in the two equations are additive inverses, that is to say:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2B3=0 ALIGN=MIDDLE  ALT=\"-3%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Just add the two equations term by term:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B3y=81 ALIGN=MIDDLE  ALT=\"5x%2B3y=81\"   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=5x-3x%2B3y-3y=81-63 ALIGN=MIDDLE  ALT=\"5x-3x%2B3y-3y=81-63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=18 ALIGN=MIDDLE  ALT=\"2x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And divide by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9 ALIGN=MIDDLE  ALT=\"x=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So there are 9 thick (5cm) books and 21 - 9 = 12 thin (3 cm)  books.\r<BR>\n" );
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document.write( "Check your answer:<BR>\n" );
document.write( "9 * 5 = 45<BR>\n" );
document.write( "12 * 3 = 36<BR>\n" );
document.write( "45 + 36 = 81:  Answer checks. </SPAN>\n" );
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