document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969458>Question 969458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two positive numbers have a difference of 17. The larger number is one more than twice the smaller. Find the two numbers. \r<BR>\n" );
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document.write( "A farmer has 162 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592352 by </B><A HREF=/tutors/aboutme.mpl?userid=erica65404><B>erica65404(394)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=erica65404><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=erica65404><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem 1:\r<BR>\n" );
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document.write( "Two positive numbers have a difference of 17. The larger number is one more than twice the smaller. Find the two numbers. \r<BR>\n" );
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document.write( "Step 1: <BR>\n" );
document.write( "write equations given the information.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=17 ALIGN=MIDDLE  ALT=\"x-y=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where x is the first positive number and y is the second positive number.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y%2B1 ALIGN=MIDDLE  ALT=\"x=2y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x has to be the larger number because the answer is a positive number <BR>\n" );
document.write( "(if x were smaller than y, the answer would be negative, for example: 10-20=-10)\r<BR>\n" );
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document.write( "I will break it up into parts\r<BR>\n" );
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document.write( "The larger number is one more than twice the smaller.<BR>\n" );
document.write( "The larger number: x<BR>\n" );
document.write( "is: =<BR>\n" );
document.write( "one more than: +1<BR>\n" );
document.write( "twice the smaller number: 2y<BR>\n" );
document.write( "This combined will give you the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y%2B1 ALIGN=MIDDLE  ALT=\"x=2y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:<BR>\n" );
document.write( "solve equations\r<BR>\n" );
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document.write( "start with the first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=17 ALIGN=MIDDLE  ALT=\"x-y=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=17%2By ALIGN=MIDDLE  ALT=\"x=17%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now you can plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2By ALIGN=MIDDLE  ALT=\"17%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all the x's in the other equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y%2B1 ALIGN=MIDDLE  ALT=\"x=2y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2By=2y%2B1 ALIGN=MIDDLE  ALT=\"17%2By=2y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now you can solve for y\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2By=2y%2B1 ALIGN=MIDDLE  ALT=\"17%2By=2y%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2By=2y ALIGN=MIDDLE  ALT=\"16%2By=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=y ALIGN=MIDDLE  ALT=\"16=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The smaller number is 16.\r<BR>\n" );
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document.write( "To find the bigger number plug 16 into our first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=17 ALIGN=MIDDLE  ALT=\"x-y=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-16=17 ALIGN=MIDDLE  ALT=\"x-16=17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=33 ALIGN=MIDDLE  ALT=\"x=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The 2 positive numbers are 33 and 16.\r<BR>\n" );
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document.write( "Problem 2:\r<BR>\n" );
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document.write( "A farmer has 162 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions?\r<BR>\n" );
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document.write( "Step 1:\r<BR>\n" );
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document.write( "Make equations given the information.\r<BR>\n" );
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document.write( "The perimeter of a rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2L%2B2W ALIGN=MIDDLE  ALT=\"P=2L%2B2W\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "we will use this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2x%2B2y ALIGN=MIDDLE  ALT=\"162=2x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where 162 is the length of the fencing available which is also the perimeter of the coral. <BR>\n" );
document.write( "x is the length and y is the width.\r<BR>\n" );
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document.write( "a rectangle that is twice as long as it is wide<BR>\n" );
document.write( "This can be translated into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "twice as long as it is wide suggests that the length (x) is going to equal (=) 2 times the width (2y)\r<BR>\n" );
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document.write( "Step 2:\r<BR>\n" );
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document.write( "solve\r<BR>\n" );
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document.write( "now that you have 2 equations you can solve for one of the variables.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2y ALIGN=MIDDLE  ALT=\"x=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can plug 2y into any place in the other equation that has x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2x%2B2y ALIGN=MIDDLE  ALT=\"162=2x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2%282y%29%2B2y ALIGN=MIDDLE  ALT=\"162=2%282y%29%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=4y%2B2y ALIGN=MIDDLE  ALT=\"162=4y%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=6y ALIGN=MIDDLE  ALT=\"162=6y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27=y ALIGN=MIDDLE  ALT=\"27=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The width is 27.<BR>\n" );
document.write( "Now plug in 27.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2x%2B2y ALIGN=MIDDLE  ALT=\"162=2x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2x%2B2%2827%29 ALIGN=MIDDLE  ALT=\"162=2x%2B2%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2x%2B54 ALIGN=MIDDLE  ALT=\"162=2x%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108=2x ALIGN=MIDDLE  ALT=\"108=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54=x ALIGN=MIDDLE  ALT=\"54=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The length is 54 and the width is 27.\r<BR>\n" );
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document.write( "*notice that the length is twice the width.\r<BR>\n" );
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document.write( "you can also check your answer to make sure you didn't make any mistakes in your calculations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2x%2B2y ALIGN=MIDDLE  ALT=\"162=2x%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=2%2854%29%2B2%2827%29 ALIGN=MIDDLE  ALT=\"162=2%2854%29%2B2%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=108%2B54 ALIGN=MIDDLE  ALT=\"162=108%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162=162 ALIGN=MIDDLE  ALT=\"162=162\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------------------<BR>\n" );
document.write( "If you have questions, please email me at ericahigley@yahoo.com. </SPAN>\n" );
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