document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149918>Question 1149918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student bought 3 boxes of pencils and 2 boxes of pens for $6. He then bought 2 boxes of pencils and 4 boxes of pens for $8. Find the cost of each box of pencils and each box of pens. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771260 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=771260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First, a solution by logical reasoning....<br><BR>\n" );
document.write( "Let's change the statement of the problem a bit so that the two purchases are by different students.  That will make it easier to describe the method for solving the problem.<br><BR>\n" );
document.write( "So we have<br><BR>\n" );
document.write( "Student A: 3 boxes of pencils and 2 boxes of pens for $6.<BR>\n" );
document.write( "Student B: 2 boxes of pencils and 4 boxes of pens for $8.<br><BR>\n" );
document.write( "Student B bought twice as many boxes of pens as student A.  So consider a third student C buying twice as much as student A, so that students B and C buy the same numbers of boxes of pens.<br><BR>\n" );
document.write( "Student C: 6 boxes of pencils and 4 boxes of pens for $12.<br><BR>\n" );
document.write( "Now compare the purchases by students B and C.  They bought the same number of boxes of pens; student C bought 4 more boxes of pencils than student B, and his cost was $4 more.  So each box of pencils costs $1.<br><BR>\n" );
document.write( "Then use the purchases of any one of the three students to find that the cost of each box of pens is $1.50.<br><BR>\n" );
document.write( "Now a typical algebraic solution, which follows the exact same path as the solution above.<br><BR>\n" );
document.write( "[1] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2y+=+6 ALIGN=MIDDLE  ALT=\"3x%2B2y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the cost of 3 boxes of pencils and 2 boxes of pens is $6<BR>\n" );
document.write( "[2] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4y+=+8 ALIGN=MIDDLE  ALT=\"2x%2B4y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the cost of 2 boxes of pencils and 4 boxes of pens is $8<br><BR>\n" );
document.write( "[3] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B4y+=+12 ALIGN=MIDDLE  ALT=\"6x%2B4y+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  double the first purchase<br><BR>\n" );
document.write( "[4] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+=+4 ALIGN=MIDDLE  ALT=\"4x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  compare purchases [2] and [3]<br><BR>\n" );
document.write( "[5] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the cost of each box of pencils is $1<br><BR>\n" );
document.write( "[6] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%29%2B2y+=+6 ALIGN=MIDDLE  ALT=\"3%281%29%2B2y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  substitute [5] into [1]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B2y+=+6 ALIGN=MIDDLE  ALT=\"3%2B2y+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+3 ALIGN=MIDDLE  ALT=\"2y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%2F2+=+1.5 ALIGN=MIDDLE  ALT=\"y+=+3%2F2+=+1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the cost of each box of pens is $1.50<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );