document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167751>Question 167751</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534432956/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am working on equations with absolute value and I need help with this word problem, please.\r<BR>\n" );
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document.write( "The problem reads:\r<BR>\n" );
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document.write( "The number of U.S. teenagers in the age category \"15-19-years olds\" during any year between 1980 and 1998 can be modeled approximately by \r<BR>\n" );
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document.write( "T=332/x-11.5/+17000\r<BR>\n" );
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document.write( "where T is the number of \"15-19-years-olds\" in thousands and x is the number of years since January 1, 1980 (U.S. Census Bureau, Current Poplulatioin Reports.) Use the model to determine the year in which the number of 15-19-year olds in the U.S. was 18,700,000 (18,700 thousands).\r<BR>\n" );
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document.write( "The book comes up with the answer of 1986 and 1996, I cant even come close to them years....please help.  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123660 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=123660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=332%2Aabs%28x-11%29%2B17000=18700 ALIGN=MIDDLE  ALT=\"332%2Aabs%28x-11%29%2B17000=18700\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=332%2Aabs%28x-11%29=1700 ALIGN=MIDDLE  ALT=\"332%2Aabs%28x-11%29=1700\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 17,000 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-11%29=5.12048 ALIGN=MIDDLE  ALT=\"abs%28x-11%29=5.12048\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 332 (this is an approximate value)\r<BR>\n" );
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document.write( "Break up the absolute value (remember, if you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29=a ALIGN=MIDDLE  ALT=\"abs%28x%29=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-a ALIGN=MIDDLE  ALT=\"x=-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   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=x-11=-5.12048 ALIGN=MIDDLE  ALT=\"x-11=-5.12048\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-11=5.12048 ALIGN=MIDDLE  ALT=\"x-11=5.12048\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-11 ALIGN=MIDDLE  ALT=\"x-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to the original value 5.12048 and it's opposite -5.12048\r<BR>\n" );
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document.write( "Now lets focus on the first equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-11=-5.12048 ALIGN=MIDDLE  ALT=\"x-11=-5.12048\"   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=x=-5.12048%2B11 ALIGN=MIDDLE  ALT=\"x=-5.12048%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 11 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.87952 ALIGN=MIDDLE  ALT=\"x=5.87952\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "So rounding to the nearest whole number, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that 6 years from the beginning (which is 1980), the population of 15-19 yr olds was 18,700,000. \r<BR>\n" );
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document.write( "So in 1986 (which is 6 years away from 1980), the population of 15-19 yr olds was 18,700,000.\r<BR>\n" );
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document.write( "Now lets focus on the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-11=5.12048 ALIGN=MIDDLE  ALT=\"x-11=5.12048\"   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=x=5.12048%2B11 ALIGN=MIDDLE  ALT=\"x=5.12048%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 11 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16.12048 ALIGN=MIDDLE  ALT=\"x=16.12048\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "So rounding to the nearest whole number, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16 ALIGN=MIDDLE  ALT=\"x=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that 16 years from the beginning (which is 1980), the population of 15-19 yr olds was 18,700,000. \r<BR>\n" );
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document.write( "So in 1996 (which is 16 years away from 1980), the population of 15-19 yr olds was 18,700,000.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So we got the solutions (after rounding to the nearest whole number) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16 ALIGN=MIDDLE  ALT=\"x=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. These solutions represented the number of years after 1980. \r<BR>\n" );
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document.write( "So in 1986 and in 1996 the population of 15-19 year olds was 18,700,000 </SPAN>\n" );
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