document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126566>Question 126566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain 18 hole golf course has par-3 par-4 and par-5 hole and there are twice as many par-4 holes as there are par-5. How many holes of each type are there if a golfer has par on every hle for a score of 70? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92721 by </B><A HREF=/tutors/aboutme.mpl?userid=marcsam823><B>marcsam823(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=marcsam823><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=92721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = number of par-3 holes<BR>\n" );
document.write( "Let y = number of par-4 holes<BR>\n" );
document.write( "Let z = number of par-5 holes<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+%2B+z+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+y+%2B+z+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > (total number of holes on the course)<BR>\n" );
document.write( "Let 3x = total number of strokes for par-3 holes<BR>\n" );
document.write( "Let 4y = total number of strokes for par-4 holes<BR>\n" );
document.write( "Let 5z = total number of strokes for par-5 holes<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4y+%2B+5z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+4y+%2B+5z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > (total strokes to par the course)<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2z ALIGN=MIDDLE  ALT=\"y+=+2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > (number of par-4 holes = twice the number of par-5 holes)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. We'll start by reducing the number of variables from 3 to 2<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+%2B+z+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+y+%2B+z+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4y+%2B+5z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+4y+%2B+5z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "We know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2z ALIGN=MIDDLE  ALT=\"y+=+2z\"   DISABLED_style= \"max-width:90%; height:auto;\" > (from above) so let's substitute for y:<BR>\n" );
document.write( "Equation 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2z+%2B+z+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+2z+%2B+z+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3z+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+3z+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4%282z%29+%2B+5z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+4%282z%29+%2B+5z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+8z+%2B+5z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+8z+%2B+5z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+13z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+13z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now we have two equations with 2 variables each:<BR>\n" );
document.write( "Equation 1 is now: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+3z+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+3z+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <BR>\n" );
document.write( "Equation 2 is now: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+13z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+13z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "We can solve for z by eliminating the x variable:<BR>\n" );
document.write( "Multiply both sides of Equation 1 by -3:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%28x+%2B+3z%29+=+-3%2818%29 ALIGN=MIDDLE  ALT=\"-3%28x+%2B+3z%29+=+-3%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x+-9z+=+-54 ALIGN=MIDDLE  ALT=\"-3x+-9z+=+-54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add this to Equation 2 and solve for z:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+13z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+13z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x+-9z+=+-54 ALIGN=MIDDLE  ALT=\"-3x+-9z+=+-54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4z+=+16 ALIGN=MIDDLE  ALT=\"4z+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+4 ALIGN=MIDDLE  ALT=\"z+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for x and y: <BR>\n" );
document.write( "We know that y = 2z<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%284%29 ALIGN=MIDDLE  ALT=\"y+=+2%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8 ALIGN=MIDDLE  ALT=\"y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We also know that x + y + z = 18<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+8+%2B+4+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+8+%2B+4+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+12+=+18 ALIGN=MIDDLE  ALT=\"x+%2B+12+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "The golf course has 6 par-3 holes, 8 par-4 holes and 4 par-5 holes\r<BR>\n" );
document.write( "\n" );
document.write( "Check:<BR>\n" );
document.write( "Let's test these results with the original equation 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B+4y+%2B+5z+=+70 ALIGN=MIDDLE  ALT=\"3x+%2B+4y+%2B+5z+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%286%29+%2B+4%288%29+%2B+5%284%29=+70 ALIGN=MIDDLE  ALT=\"3%286%29+%2B+4%288%29+%2B+5%284%29=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%2B+32+%2B+20+=+70 ALIGN=MIDDLE  ALT=\"18+%2B+32+%2B+20+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70+=+70 ALIGN=MIDDLE  ALT=\"70+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This checks. Our answers are correct.<BR>\n" );
document.write( "18 + 32 + 20 = 70\r<BR>\n" );
document.write( "\n" );
document.write( "           <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );