document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340360>Question 340360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?\r<BR>\n" );
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document.write( "A. 23 B. 25 C. 50  D. 75  E. 94 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243882 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=243882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?\r<BR>\n" );
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document.write( "A. 23 B. 25 C. 50  D. 75  E. 94\r<BR>\n" );
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document.write( "sum -1 to -22 --> same as sum of 1 to 22 but multiply result by -1<BR>\n" );
document.write( "sum 1 to 22 = 1/2 * n * (n + 1) = 1/2 * 22 * 23 = 506/2 = 253<BR>\n" );
document.write( "sum -1 to -22 = -253<BR>\n" );
document.write( "so sum -22 to 22 = 0\r<BR>\n" );
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document.write( "what range of positive integers adds to 253 + 72 = 325 ?\r<BR>\n" );
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document.write( "1/2 * n * (n + 1) = 325<BR>\n" );
document.write( "1/2 * (n^2 + n) = 325<BR>\n" );
document.write( "n^2 + n = 650 (multiplied both sides by 2)<BR>\n" );
document.write( "n^2 + n - 650 = 0\r<BR>\n" );
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document.write( "factor 650:<BR>\n" );
document.write( "650 = 10 * 65 = 10 * 13 * 5 = 2 * 5 * 5 * 13 = 25 * 26\r<BR>\n" );
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document.write( "check factors:<BR>\n" );
document.write( "(n - 25)(n + 26) --> FOIL (First Inner Outer Last) --> n^2 + 26n - 25n - 650<BR>\n" );
document.write( "n = 25 or n = -26, throw negative result out<BR>\n" );
document.write( "so:<BR>\n" );
document.write( "1 to 25 adds to 325\r<BR>\n" );
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document.write( "answer is B. 25<BR>\n" );
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