document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168273>Question 1168273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tom and Jerry are selling fruit for a charity fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Tom sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Jerry sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each  of one small box of oranges and one large box of oranges.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792904 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=792904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "This is a good problem for demonstrating that the formal algebraic solution follows exactly the same path as an informal solution using logical reasoning and simple arithmetic.<br><BR>\n" );
document.write( "(1) Given:<BR>\n" );
document.write( "3 small and 14 large sell for $203<BR>\n" );
document.write( "11 small and 11 large sell for $220<br><BR>\n" );
document.write( "Algebraically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B14y+=+203 ALIGN=MIDDLE  ALT=\"3x%2B14y+=+203\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2B11y+=+220 ALIGN=MIDDLE  ALT=\"11x%2B11y+=+220\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) Logical reasoning: if 11 of each cost $220, then 1 of each costs $220/11 = $20.<br><BR>\n" );
document.write( "Algebraically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B14y+=+203 ALIGN=MIDDLE  ALT=\"3x%2B14y+=+203\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11x%2F11%2B11y%2F11+=+220%2F11 ALIGN=MIDDLE  ALT=\"11x%2F11%2B11y%2F11+=+220%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By+=+20 ALIGN=MIDDLE  ALT=\"x%2By+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(3) Logical reasoning: if 1 of each costs $20, then 3 of each cost $60.<br><BR>\n" );
document.write( "Algebraically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B14y+=+203 ALIGN=MIDDLE  ALT=\"3x%2B14y+=+203\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3y+=+60 ALIGN=MIDDLE  ALT=\"3x%2B3y+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(4) Logical reasoning: If the numbers of small boxes are the same, then the difference in cost is because of the difference in the numbers of large boxes.  The difference in cost is $143; that is because of the 11 additional large boxes.<br><BR>\n" );
document.write( "Algebraically (subtracting one equation from the other):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11y+=+143 ALIGN=MIDDLE  ALT=\"11y+=+143\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(5) Logical reasoning: If 11 large boxes cost $143, then each large box costs $143/11 = $13.<br><BR>\n" );
document.write( "Algebraically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11y%2F11+=+143%2F11 ALIGN=MIDDLE  ALT=\"11y%2F11+=+143%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+13 ALIGN=MIDDLE  ALT=\"y+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(6) Logical reasoning: 1 of each costs $20; and the large box costs $13; so the small box costs $20-13 = 7.<br><BR>\n" );
document.write( "Algebraically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B13+=+20 ALIGN=MIDDLE  ALT=\"x%2B13+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20-13+=+7 ALIGN=MIDDLE  ALT=\"x+=+20-13+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "large box: $13<BR>\n" );
document.write( "small box: $7<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );