document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=228139>Question 228139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which three consecutive integers have a product that is 800 times their sum? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #169423 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=169423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which three consecutive integers have a product that is 800 times their sum?\r<BR>\n" );
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document.write( "Step 1.  Let n be the first integer.\r<BR>\n" );
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document.write( "Step 2.  Let n+1 and n+2 be the next two consecutive integers.\r<BR>\n" );
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document.write( "Step 3.  Let n+n+1+n+2=3n+3=3(n+1) be the sum of the three consecutive integers.\r<BR>\n" );
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document.write( "Step 4.  Let n(n+1)(n+2) be the product of the three consecutive integers\r<BR>\n" );
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document.write( "Step 5.  Then,n(n+1)(n+2)=800*3(n+1) since the product in Step 4 is 800 times their sum in Step 3.\r<BR>\n" );
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document.write( "Step 6.  Solving n(n+1)(n+2)=800*3(n+1) yields the following steps:\r<BR>\n" );
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document.write( "Simplify by dividing n+1 to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%28n%2B2%29%29%2A%281%2F%28n%2B1%29%29=2400%28n%2B1%29%2A%281%2F%28n%2B1%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n=2400 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n=2400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 2400 from both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-2400=2400-2400 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-2400=2400-2400\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-2400=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-2400=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 7.  To solve, we can factor as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-2400=%28x%2B50%29%28x-48%29=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-2400=%28x%2B50%29%28x-48%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "This implies that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B50%29=0 ALIGN=MIDDLE  ALT=\"x%2B50%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-50 ALIGN=MIDDLE  ALT=\"x=-50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-48%29=90 ALIGN=MIDDLE  ALT=\"x-48%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=48 ALIGN=MIDDLE  ALT=\"x=48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We also could have use the quadratic formula given as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where a = 1, b=2, and c=-2400.\r<BR>\n" );
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document.write( "Step 9.  With n=48, then n+1=49 and n+2=50.  Check the relationship in Step 5 n(n+1)(n+2)=800(n+n+1+n+2) with these values.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2A49%2A50=800%2848%2B49%2B50%29 ALIGN=MIDDLE  ALT=\"48%2A49%2A50=800%2848%2B49%2B50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=117600=117600 ALIGN=MIDDLE  ALT=\"117600=117600\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is a true statement.\r<BR>\n" );
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document.write( "Step 10.  With n=-50, then n+1=-49 and n+2=-48.  Check the relationship in Step 5 n(n+1)(n+2)=800(n+n+1+n+2) with these values.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-48%29%2A%28-49%29%2A%28-50%29=800%28-48%2B%28-49%29%2B%28-50%29%29 ALIGN=MIDDLE  ALT=\"%28-48%29%2A%28-49%29%2A%28-50%29=800%28-48%2B%28-49%29%2B%28-50%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-117600=-117600 ALIGN=MIDDLE  ALT=\"-117600=-117600\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is a true statement.\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  There are two sets of consecutive numbers.  The first set is 48, 49, 50 and the second set is -48, -49, -50.\r<BR>\n" );
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document.write( "I hope the above steps were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( " </SPAN>\n" );
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