document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211262>Question 211262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive integers such that the sum of the first plus one-third of the second plus three-fourths of the third is 31.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159682 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive integers such that the sum of the first plus one-third of the second plus three-fourths of the third is 31. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the 1st number be F<BR>\n" );
document.write( "Then the 2nd and 3rd numbers are (F + 1) and (F + 2), respectively\r<BR>\n" );
document.write( "\n" );
document.write( "Since the sum of the 1st, one-third of the second, and three-fourths of the 3rd is 31, <BR>\n" );
document.write( "then:	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F++%2B++%281%2F3%29%2A%28F+%2B+1%29+%2B++%283%2F4%29%2A%28F+%2B+2%29+=+31 ALIGN=MIDDLE  ALT=\"F++%2B++%281%2F3%29%2A%28F+%2B+1%29+%2B++%283%2F4%29%2A%28F+%2B+2%29+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" >		 \r<BR>\n" );
document.write( "\n" );
document.write( "Multiply the equation by the LCD, 12 to get:	12F + 4F + 4 + 9F + 18  =  372<BR>\n" );
document.write( "25F  =  350\r<BR>\n" );
document.write( "\n" );
document.write( "F = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350%2F25 ALIGN=MIDDLE  ALT=\"350%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = 14\r<BR>\n" );
document.write( "\n" );
document.write( "Since F, or the 1st number is 14, the 3 consecutive integers are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2814_15_and_16%29 ALIGN=MIDDLE  ALT=\"highlight_green%2814_15_and_16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "------------------<BR>\n" );
document.write( "Check<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The 1st, plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of 15 (the second), plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > of 16 (the 3rd number) equals 31, or,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+%2B+%281%2F3%29%2A15+%2B+%283%2F4%29%2A16+=+31 ALIGN=MIDDLE  ALT=\"14+%2B+%281%2F3%29%2A15+%2B+%283%2F4%29%2A16+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14+%2B+5+%2B+12+=+31 ALIGN=MIDDLE  ALT=\"14+%2B+5+%2B+12+=+31\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "31 = 31 (TRUE)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );