document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157772>Question 157772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116257 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=116257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,Hope I can help<BR>\n" );
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document.write( "Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen.<BR>\n" );
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document.write( "consecutive means \" in order\"(examples: 45,46,47,48 . Sunday, Monday, Tuesday)<BR>\n" );
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document.write( "To find the 4 consecutive numbers, we have to find the variables for all four numbers<BR>\n" );
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document.write( "Since consecutive means \" in order \"(we are trying to find 4 numbers that come right after the other(example of consecutive numbers: 22,23,24,25,26)<BR>\n" );
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document.write( "We can always name the first number of any \"consecutive numbers\" - \"x\"<BR>\n" );
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document.write( "\"x\" is our first number, to find the other numbers, we will add \"1\" each time(we are trying to find numbers that come right after the other)<BR>\n" );
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document.write( "2nd number = (add \"1\" to our first number \"x\") = \"x+1\"<BR>\n" );
document.write( "3rd number = (add \"1\" to the second number \"x + 1\", (\"x + 1 + 1\")) = \"x+2\"<BR>\n" );
document.write( "4th number = (add \"1\" to the third number \"x+2\",(\"x+2+1\")) = \"x+3\"<BR>\n" );
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document.write( "(If there was a fifth number you would add \"1\" to the fourth number \"x+3\" = \"x+4\", the sixth number would be \"1\" added to the fifth number \"x+4\" = \"x+5\", you get the idea)(If you were solving for consecutive odd or even numbers, you would add \"2\" every time, consecutive even/odd number = ( x, x + 2, x + 4, x + 6, x + 8, ...)<BR>\n" );
document.write( "(examples of consecutive even/odd number: 3, 5, 7, 9 : 16, 18, 20, 22))<BR>\n" );
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document.write( "Since we are solving for just consecutive numbers, our numbers are<BR>\n" );
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document.write( "1st number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
document.write( "2nd number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
document.write( "3rd number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
document.write( "4th number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
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document.write( "Now we can replace these variables with the problem, and solve for the numbers<BR>\n" );
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document.write( "Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen.<BR>\n" );
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document.write( "If we replace the variables in the problem, and put the word problem in an equation, the equation = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+ ALIGN=MIDDLE  ALT=\"+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we just solve for \"x\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+ ALIGN=MIDDLE  ALT=\"+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will remove the first set of parentheses,we will multiply 2(x)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+ ALIGN=MIDDLE  ALT=\"+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29+-+2x+=+16+ ALIGN=MIDDLE  ALT=\"+%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29+-+2x+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will remove the other sets of parentheses<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29+-+2x+=+16+ ALIGN=MIDDLE  ALT=\"+%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29+-+2x+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B1%2Bx%2B2%2Bx%2B3+-+2x+=+16+ ALIGN=MIDDLE  ALT=\"+x%2B1%2Bx%2B2%2Bx%2B3+-+2x+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will rearrange the equation, so we can add/subtract like terms<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B1%2Bx%2B2%2Bx%2B3+-+2x+=+16+ ALIGN=MIDDLE  ALT=\"+x%2B1%2Bx%2B2%2Bx%2B3+-+2x+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2Bx%2Bx-2x%2B1%2B2%2B3+=+16+ ALIGN=MIDDLE  ALT=\"+x%2Bx%2Bx-2x%2B1%2B2%2B3+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will add/subtract like terms<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2Bx%2Bx-2x%2B1%2B2%2B3+=+16+ ALIGN=MIDDLE  ALT=\"+x%2Bx%2Bx-2x%2B1%2B2%2B3+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > =, (x+x+x-2x)(+1+2+3) = 16, = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6+=+16+ ALIGN=MIDDLE  ALT=\"+x%2B6+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To solve for \"x\" we will move \"6\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6+=+16+ ALIGN=MIDDLE  ALT=\"+x%2B6+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B6+-+6+=+16+-+6+ ALIGN=MIDDLE  ALT=\"+x%2B6+-+6+=+16+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+16+-+6+ ALIGN=MIDDLE  ALT=\"+x+=+16+-+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+10+ ALIGN=MIDDLE  ALT=\"+x+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"x\" = \"10\" , we can check by replacing \"x\" with our equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+ ALIGN=MIDDLE  ALT=\"+%28%28x%2B1%29%2B%28x%2B2%29%2B%28x%2B3%29%29+-+2%28x%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28%2810%29%2B1%29%2B%28%2810%29%2B2%29%2B%28%2810%29%2B3%29%29+-+2%2810%29+=+16+ ALIGN=MIDDLE  ALT=\"+%28%28%2810%29%2B1%29%2B%28%2810%29%2B2%29%2B%28%2810%29%2B3%29%29+-+2%2810%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28%2810%29%2B1%29%2B%28%2810%29%2B2%29%2B%28%2810%29%2B3%29%29+-+2%2810%29+=+16+ ALIGN=MIDDLE  ALT=\"+%28%28%2810%29%2B1%29%2B%28%2810%29%2B2%29%2B%28%2810%29%2B3%29%29+-+2%2810%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2810%2B1%29%2B%2810%2B2%29%2B%2810%2B3%29%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%28%2810%2B1%29%2B%2810%2B2%29%2B%2810%2B3%29%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2810%2B1%29%2B%2810%2B2%29%2B%2810%2B3%29%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%28%2810%2B1%29%2B%2810%2B2%29%2B%2810%2B3%29%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2811%29%2B%2812%29%2B%2813%29%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%28%2811%29%2B%2812%29%2B%2813%29%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%2811%29%2B%2812%29%2B%2813%29%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%28%2811%29%2B%2812%29%2B%2813%29%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2811%2B12%2B13%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%2811%2B12%2B13%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2836%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%2836%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+36+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16+=+16+ ALIGN=MIDDLE  ALT=\"+16+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True)<BR>\n" );
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document.write( "Here is our number variables again (To find the numbers, replace \"x\" with \"10\")<BR>\n" );
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document.write( "1st number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
document.write( "2nd number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%29+%2B+1+ ALIGN=MIDDLE  ALT=\"+%2810%29+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B1 ALIGN=MIDDLE  ALT=\"10%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
document.write( "3rd number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%29+%2B+2+ ALIGN=MIDDLE  ALT=\"+%2810%29+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B2 ALIGN=MIDDLE  ALT=\"10%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
document.write( "4th number = \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810%29+%2B+3+ ALIGN=MIDDLE  ALT=\"+%2810%29+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B3 ALIGN=MIDDLE  ALT=\"10%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\", \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"<BR>\n" );
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document.write( "Find four consecutive integers such that twice the first subtracted from the sum of the other three integers is sixteen. ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2811+%2B+12+%2B+13%29+-+2%2810%29+=+16+ ALIGN=MIDDLE  ALT=\"+%2811+%2B+12+%2B+13%29+-+2%2810%29+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2836%29+-+20+=+16+ ALIGN=MIDDLE  ALT=\"+%2836%29+-+20+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36-20=16+ ALIGN=MIDDLE  ALT=\"+36-20=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=16 ALIGN=MIDDLE  ALT=\"16=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > (True))<BR>\n" );
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document.write( "1st number = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+ ALIGN=MIDDLE  ALT=\"+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd number = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3rd number = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4th number = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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