document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=973229>Question 973229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the smallest of three consecutive positive numbers if the product of the first and third is one less than eight times the second? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595482 by </B><A HREF=/tutors/aboutme.mpl?userid=crystal5213><B>crystal5213(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=crystal5213><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=595482\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The smallest number is equal to 7.\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "For this problem, I'll be using variables to represent the numbers: x, y, and z. But since they are consecutive, y=x+1, and z=x+2, so the numbers can be written as x, x+1, and x+2. \r<BR>\n" );
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document.write( "According to the problem, the product of the first and third number (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x ALIGN=MIDDLE  ALT=\"x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is equal to one less than eight times the second number (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%28x%2B1%29-1%29 ALIGN=MIDDLE  ALT=\"8%28x%2B1%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%2B7 ALIGN=MIDDLE  ALT=\"8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "We can set the problem up like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x=8x%2B7 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x=8x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can solve it like an algebraic equation instead of a word problem. Start by moving the variable to one side of the equation by subtracting 8x from both sides, resulting in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x=7 ALIGN=MIDDLE  ALT=\"x%5E2-6x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since there is a variable squared, we should use the quadratic formula. So we will have to subtract 7 as well, so that 0 will be on one side of the equal sign.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x-7=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "According to the quadratic equation, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC=0%2C ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC=0%2C\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, we plug in the numbers.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A%28-7%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A%28-7%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in this case, a equals one because there is no number before <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the coefficient must be 1. b is -6 since that is the coefficient for x, and c is -7.<BR>\n" );
document.write( "Finally, after using a calculator to solve the equation, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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