document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039513>Question 1039513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Eleven less than two third of twice the number and 19 is 95.find the number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654279 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number.\r<BR>\n" );
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document.write( "2/3 * the number and 19 is equal to 2/3 * (x + 19).\r<BR>\n" );
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document.write( "11 less than that is equal to 2/3 * (x + 19) - 11.\r<BR>\n" );
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document.write( "you get 2/3 * (x + 19) - 11 = 95.\r<BR>\n" );
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document.write( "add 11 to both sides of the equation to get 2/3 * (x + 19) = 106.\r<BR>\n" );
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document.write( "multiply both sides of the equation by 3/2 to get x + 19 = 3/2 * 106.\r<BR>\n" );
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document.write( "simplify this to get x + 19 = 159.\r<BR>\n" );
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document.write( "subtract 19 from both sides of the equation to get x = 140.\r<BR>\n" );
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document.write( "that should be your number.\r<BR>\n" );
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document.write( "your original equation is 2/3 * (x + 19) - 11 = 95.\r<BR>\n" );
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document.write( "if the number is 140, then 2/3 * (140 + 19) - 11 = 95.\r<BR>\n" );
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document.write( "do the math and you get 95 = 95 which confirms the solution is correct as long as the original equation is correct.\r<BR>\n" );
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document.write( "interpretation of the original problem statement is the key.\r<BR>\n" );
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document.write( "the original problem statement says:\r<BR>\n" );
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document.write( "Eleven less than two third of twice the number and 19 is 95.  find the number.\r<BR>\n" );
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document.write( "this can be interpreted as:\r<BR>\n" );
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document.write( "2/3 * 2x + 19 - 11, ...\r<BR>\n" );
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document.write( "or it can be interpreted as:\r<BR>\n" );
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document.write( "2/3 * 2 * (x + 19) - 11.\r<BR>\n" );
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document.write( "the first interpretation didn't make a lot of sense because why would you add 19 and then subtract 11 and it also led to an answer that was not an integer,\r<BR>\n" );
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document.write( "the second interpretation made more sense and did lead to an integer answer.\r<BR>\n" );
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document.write( "the answer is that the number had to be 140 because 2/3 * (140 + 19) - 11 is equal to 95.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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