document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=582661>Question 582661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sorry, but I have to repeat the other question I have put because I need the equation to only use ONE variable, to be able to be solved by hand: \r<BR>\n" );
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document.write( "There are three types of bikes. A bicycle, tricycle, and tandem bikes. A bicycle as 2 wheels, 2 pedals, and 1 seat. A tricycle has 3 wheels, 2 pedals, and 1 seat. A tandem bike has 2 wheels, 4 pedals, and 2 seats. <BR>\n" );
document.write( "How many of each are there if there are 144 front steering handlebars, 378 pedals, and 320 wheels? How many bicycles, tricycles, and tandem bikes? <BR>\n" );
document.write( "Can you tell me the equation to find it? It's been bugging me for a while.\r<BR>\n" );
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document.write( "Ex: 2x + 2(320 - x) + ? = # of bikes or something.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372168 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can do one variable at a  time, but you need to find three numbers that mean different things (number of bicycles, number of tricycles, and number of tandem bikes), so I would rather use three different letter for those numbers. We could re-use old traditional x, for each part of the problemm, but it could get confusing.<BR>\n" );
document.write( "The total number of bikes is the number of front steering handlebars: 144.<BR>\n" );
document.write( "How many tricycles?<BR>\n" );
document.write( "Tricycles are the only bikes with 3 wheels. All the other bikes have 2.<BR>\n" );
document.write( "So if we call the number of tricycles x, the number of other bikes (bicycles and tandem bikes) will be 144-x<BR>\n" );
document.write( "The number of wheels will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2%28144-x%29=320 ALIGN=MIDDLE  ALT=\"3x%2B2%28144-x%29=320\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's find x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B2%28144-x%29=320 ALIGN=MIDDLE  ALT=\"3x%2B2%28144-x%29=320\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B288-2x=320 ALIGN=MIDDLE  ALT=\"3x%2B288-2x=320\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (applying distributive property)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B288-2x=320 ALIGN=MIDDLE  ALT=\"3x%2B288-2x=320\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-2%29x%2B288=320 ALIGN=MIDDLE  ALT=\"%283-2%29x%2B288=320\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B288=320 ALIGN=MIDDLE  ALT=\"x%2B288=320\"   DISABLED_style= \"max-width:90%; height:auto;\" > (collecting like terms, which is also the distributive property)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B288=320 ALIGN=MIDDLE  ALT=\"x%2B288=320\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B288-288=320-288 ALIGN=MIDDLE  ALT=\"x%2B288-288=320-288\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=32%29 ALIGN=MIDDLE  ALT=\"highlight%28x=32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "How many tandem bikes?<BR>\n" );
document.write( "Tandem bikes have 4 pedals, while all the other bikes have just 2.<BR>\n" );
document.write( "Do you want to call the number of tandem bikes y? We could call it x, if we remember that we are recycling and this x is not the same x as before, but I'd rather use a different letter.<BR>\n" );
document.write( "If the number of tandem bikes is y, the number of other bikes (bicycles and tricycles) is 144-y.<BR>\n" );
document.write( "The total number of pedals is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B2%28144-y%29=378 ALIGN=MIDDLE  ALT=\"4y%2B2%28144-y%29=378\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's find y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B2%28144-y%29=378 ALIGN=MIDDLE  ALT=\"4y%2B2%28144-y%29=378\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B288-2y=378 ALIGN=MIDDLE  ALT=\"4y%2B288-2y=378\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-2%29y%2B288=378 ALIGN=MIDDLE  ALT=\"%284-2%29y%2B288=378\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B288=378 ALIGN=MIDDLE  ALT=\"2y%2B288=378\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B288-288=378-288 ALIGN=MIDDLE  ALT=\"2y%2B288-288=378-288\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=90 ALIGN=MIDDLE  ALT=\"2y=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2F2=90%2F2 ALIGN=MIDDLE  ALT=\"2y%2F2=90%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=45%29 ALIGN=MIDDLE  ALT=\"highlight%28y=45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we know there are 32 tricycles and 45 tandem bikes.<BR>\n" );
document.write( "How many bicycles.<BR>\n" );
document.write( "If z is the number of bicycles, the total number of bikes is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B32%2B45=144 ALIGN=MIDDLE  ALT=\"z%2B32%2B45=144\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B77=144 ALIGN=MIDDLE  ALT=\"z%2B77=144\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2B77-77=144-77 ALIGN=MIDDLE  ALT=\"z%2B77-77=144-77\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28z=67%29 ALIGN=MIDDLE  ALT=\"highlight%28z=67%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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