document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058559>Question 1058559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the atomic number of two elements is not more than 22, with an average 11 and with a difference less than 16. What are the possible atomic numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673643 by </B><A HREF=/tutors/aboutme.mpl?userid=solve_for_x><B>solve_for_x(190)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solve_for_x><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=673643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x represent one atomic number, and let y represent the other.\r<BR>\n" );
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document.write( "Since the sum is not more than 22, you can write:\r<BR>\n" );
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document.write( "x + y &#8804; 22\r<BR>\n" );
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document.write( "Since the average is equal to 11, you can write:\r<BR>\n" );
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document.write( "(x + y)/2 = 11\r<BR>\n" );
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document.write( "which can be rearranged as:\r<BR>\n" );
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document.write( "x + y = 2(11)\r<BR>\n" );
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document.write( "x + y = 22\r<BR>\n" );
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document.write( "Thus, the sum is not only \"not more than 22\", is must be exactly 22.\r<BR>\n" );
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document.write( "Then, since the difference is less than 16, you can write:\r<BR>\n" );
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document.write( "x - y < 16\r<BR>\n" );
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document.write( "Solving x + y = 22 for y gives:\r<BR>\n" );
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document.write( "y = 22 - x\r<BR>\n" );
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document.write( "Substituting that into the inequality gives:\r<BR>\n" );
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document.write( "x - (22 - x) < 16\r<BR>\n" );
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document.write( "x - 22 + x < 16\r<BR>\n" );
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document.write( "2x - 22 < 16\r<BR>\n" );
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document.write( "2x < 16 + 22\r<BR>\n" );
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document.write( "2x < 38\r<BR>\n" );
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document.write( "x < 19\r<BR>\n" );
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document.write( "Then, solving x + y = 22 for x gives:\r<BR>\n" );
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document.write( "x = 22 - y\r<BR>\n" );
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document.write( "Substituting this into inequality gives:\r<BR>\n" );
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document.write( "22 - y - y < 16\r<BR>\n" );
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document.write( "22 - 2y < 16\r<BR>\n" );
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document.write( "-2y < 16 - 22\r<BR>\n" );
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document.write( "-2y < -6\r<BR>\n" );
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document.write( "y > 3  (remember to reverse the inequality sign when multiplying or dividing by a negative number)\r<BR>\n" );
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document.write( "Thus, the combinations must have x < 19 and y > 3\r<BR>\n" );
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document.write( "The set of combinations is then:\r<BR>\n" );
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document.write( "(4, 18), (5, 17), (6, 16), (7, 15), (8, 14), (9, 13), (10, 12), and (11, 11) </SPAN>\n" );
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