document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146978>Question 146978</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five pencils and three erasers cost 65 cents. Three pencils and two erasers cost 40 cents. Find the cost of one pencil and the cost of one eraser.  <BR>\n" );
document.write( "So far I've got: 5p + 3e = .65 and  3p + 2e = .40  but don't know where to go from here to reach the answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107319 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at it this way.<BR>\n" );
document.write( "You have a system of equations.<BR>\n" );
document.write( "Two equations with two unknowns, p and e. <BR>\n" );
document.write( "You can solve the system to find p and e. <BR>\n" );
document.write( "5p + 3e = .65<BR>\n" );
document.write( "3p + 2e = .40<BR>\n" );
document.write( "There are several methods you can use to solve this system of equations.<BR>\n" );
document.write( "We'll use the substitution method.<BR>\n" );
document.write( "First off, let's multiply both sides by 100 to get rid of the decimal.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500p%2B300e=65 ALIGN=MIDDLE  ALT=\"500p%2B300e=65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p%2B200e=40 ALIGN=MIDDLE  ALT=\"300p%2B200e=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can use equation 1 to get 300p in terms of e and substitute into eq.2,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500p%2B300e=65 ALIGN=MIDDLE  ALT=\"500p%2B300e=65\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500p=65-300e ALIGN=MIDDLE  ALT=\"500p=65-300e\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p=%2865-300e%29%283%2F5%29 ALIGN=MIDDLE  ALT=\"300p=%2865-300e%29%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply both sides by (3/5). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p=39-180e ALIGN=MIDDLE  ALT=\"300p=39-180e\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute that value into equation 2 and solve for e.<BR>\n" );
document.write( "2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p%2B200e=40 ALIGN=MIDDLE  ALT=\"300p%2B200e=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839-180e%29%2B200e=40 ALIGN=MIDDLE  ALT=\"%2839-180e%29%2B200e=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20e=1 ALIGN=MIDDLE  ALT=\"20e=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=0.05 ALIGN=MIDDLE  ALT=\"e=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you can use either equation to solve for p. I chose equation 2. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p%2B200e=40 ALIGN=MIDDLE  ALT=\"300p%2B200e=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p%2B200%280.05%29=40 ALIGN=MIDDLE  ALT=\"300p%2B200%280.05%29=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p%2B10=40 ALIGN=MIDDLE  ALT=\"300p%2B10=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300p=30 ALIGN=MIDDLE  ALT=\"300p=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=0.10 ALIGN=MIDDLE  ALT=\"p=0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the pencil costs a dime and the eraser costs a nickel.<BR>\n" );
document.write( "You can check your answers by using your original equations.<BR>\n" );
document.write( "5p + 3e = .65<BR>\n" );
document.write( "5(0.10)+3(0.05)=.65<BR>\n" );
document.write( "0.50+0.15=0.65<BR>\n" );
document.write( "0.65=0.65<BR>\n" );
document.write( "True<BR>\n" );
document.write( "3p + 2e = .40<BR>\n" );
document.write( "3(0.10)+2(0.05)=0.40<BR>\n" );
document.write( "0.30+0.10=0.40<BR>\n" );
document.write( "0.40=0.40<BR>\n" );
document.write( "True<BR>\n" );
document.write( "Your answers led to true statements.<BR>\n" );
document.write( "They are good answers. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );