document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237201>Question 237201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Have 2 questions.\r<BR>\n" );
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document.write( "Question 1)  The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace is &#8730;6 m. Find the width and the height.\r<BR>\n" );
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document.write( "Question 2)  The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174560 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174560\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question 1) The width of a rectangular gate is 2 meters (m) larger than its height. <BR>\n" );
document.write( "The diagonal brace is &#8730;6 m. Find the width and the height.<BR>\n" );
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document.write( "Let x = the height<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+2) = the width<BR>\n" );
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document.write( "using pythag a^2 + b^2 = c^2<BR>\n" );
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document.write( "x^2 + (x+2)^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%286%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%286%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "x^2 + x^2 + 4x + 4 = 6<BR>\n" );
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document.write( "2x^2 + 4x + 4 - 6 = 0<BR>\n" );
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document.write( "2x^2 + 4x - 2 = 0<BR>\n" );
document.write( "Simplify divide by 2<BR>\n" );
document.write( "x^2 + 2x - 1 = 0<BR>\n" );
document.write( "Use the quadratic formula to find the positive solution:<BR>\n" );
document.write( "<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( "In this problem a=1; b=2; c=-1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%284-+%28-4%29+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%284-+%28-4%29+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%284+%2B+4+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%284+%2B+4+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%288+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%288+%29%29%2F%282%29+\"   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=x+=+%28-2+%2B+2.828%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B+2.828%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.828%2F2 ALIGN=MIDDLE  ALT=\".828%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = .414 meters is the height, 2.414 meters is the width<BR>\n" );
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document.write( "Check solution on a calc: enter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28.414%5E2+%2B+2.414%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28.414%5E2+%2B+2.414%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.45 ~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( ";\r<BR>\n" );
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document.write( "Question 2) The members of a flying club plan to share equally the cost of a $200,000 airplane.<BR>\n" );
document.write( " The members want to find five more people to join the club so that the cost per person will decrease by $2000.<BR>\n" );
document.write( " How many members are currently in the club?<BR>\n" );
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document.write( "Let x = no. of members in the club now<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+5) = no. of members to decrease cost per person by 2k<BR>\n" );
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document.write( "To reduce typing lets do this in \"thousands of dollars\"<BR>\n" );
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document.write( "Current cost per member: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fx ALIGN=MIDDLE  ALT=\"200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "current cost - more member cost = 2 thousand<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fx ALIGN=MIDDLE  ALT=\"200%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "Multiply equation by x(x+5); results:<BR>\n" );
document.write( "200(x+5) - 200x = 2x(x+5)<BR>\n" );
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document.write( "200x + 1000 - 200x = 2x^2 + 10x<BR>\n" );
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document.write( "1000 = 2x^2 + 10x<BR>\n" );
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document.write( "A quadratic equation<BR>\n" );
document.write( "2x^2 + 10x - 1000 = 0<BR>\n" );
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document.write( "Simplify, divide by 2<BR>\n" );
document.write( "x^2 + 5x - 500 = 0<BR>\n" );
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document.write( "Factors easily to<BR>\n" );
document.write( "(x+25)(x-20) = 0<BR>\n" );
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document.write( "Positive solution<BR>\n" );
document.write( "x = 20 members currently<BR>\n" );
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document.write( "Check solution:<BR>\n" );
document.write( "200/20 = 10 thousand per member<BR>\n" );
document.write( "200/25 = 8 thousand per member<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Saving: 2k per member\r<BR>\n" );
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document.write( " </SPAN>\n" );
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