document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=317391>Question 317391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simon Rose surveyed feature films released from 1983 through 1993, listing the most common names of movie characters.  The list is shown here, but the number of characters with the names Jack and John is omitted.  Combined, there were 230 movie characters with these names.  Taking triple the number of Jack characters and subtracting double the number of John characters gives 16 less than triple the number of George characters.  How many movie characters had the names Jack and John from 1983 through 1993?<BR>\n" );
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document.write( "Name                Characters<BR>\n" );
document.write( "Jack                     ?<BR>\n" );
document.write( "John                     ?<BR>\n" );
document.write( "Frank                    87<BR>\n" );
document.write( "Harry                    72<BR>\n" );
document.write( "David                    63<BR>\n" );
document.write( "George                 62<BR>\n" );
document.write( "Michael                59<BR>\n" );
document.write( "Tom                     59<BR>\n" );
document.write( "Mary                    54<BR>\n" );
document.write( "Paul                     53<BR>\n" );
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document.write( "The calorie - nutrient information for an apple and an avocado is given in the table.  How many of each should be eaten to get exactly 1000 calories and 100 grams of carbohydrates?<BR>\n" );
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document.write( "                                              One Apple                            One Avocado<BR>\n" );
document.write( "Calories                                        100                                    350<BR>\n" );
document.write( "Carbohydrates (grams)                   24                                        14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #227256 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=227256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the number of Jack characters and let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> represent the number of John characters.  Then from the data given we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 230\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x\ -\ 2y\ =\ 170\">\r<BR>\n" );
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document.write( "Solve the system for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x,y)\">\r<BR>\n" );
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document.write( "Hint:  Multiply the first equation by 2 and solve by elimination.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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