document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=223687>Question 223687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A movie theater charges $7.50 for adutls and $4.50 for children. The receipts for one showing of a movie were $540. If 80 tickets were sold, find how many tickets of each type were sold. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167248 by </B><A HREF=/tutors/aboutme.mpl?userid=MLipsky><B>MLipsky(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MLipsky><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=167248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I came up with a 6-step method for solving word problems:<BR>\n" );
document.write( "1.  Draw a picture.<BR>\n" );
document.write( "2.  Assign variables to all unknowns.<BR>\n" );
document.write( "3.  Write any relevant formulas.<BR>\n" );
document.write( "4.  Write an equation.<BR>\n" );
document.write( "5.  Solve the equation.<BR>\n" );
document.write( "6.  Check your solution.\r<BR>\n" );
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document.write( "<hr />1.  Draw a picture.<BR>\n" );
document.write( "(This is very useful for problems with shapes, distance, or combining mixtures.)\r<BR>\n" );
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document.write( "In this problem, drawing a picture probably wouldn't help.\r<BR>\n" );
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document.write( "<hr />2.  Assign variables to all unknowns.<BR>\n" );
document.write( "(The unknowns are usually what the question asks for, in the last part of the problem.)\r<BR>\n" );
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document.write( "The last part of the problem says, \"find how many tickets of each type were sold.\"  So we need variables for each type of ticket.\r<BR>\n" );
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document.write( "Let a = number of adult tickets.<BR>\n" );
document.write( "Let c = number of child tickets.\r<BR>\n" );
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document.write( "<hr />3.  Write any relevant formulas.<BR>\n" );
document.write( "(Do you need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve this problem?  How about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  Write them down.)\r<BR>\n" );
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document.write( "In this problem, there aren't any relevant formulas.\r<BR>\n" );
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document.write( "<hr />4.  Write an equation.\r<BR>\n" );
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document.write( "The problem says, \"80 tickets were sold\".  So . . . <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=80 ALIGN=MIDDLE  ALT=\"a%2Bc=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "WARNING:  a very common mistake in this problem would be to write . . . <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=540 ALIGN=MIDDLE  ALT=\"a%2Bc=540\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " . . . But \"a\" and \"c\" are the number of tickets sold, and the problem does not say that 540 tickets were sold.  So what do we do with the rest of the numbers?\r<BR>\n" );
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document.write( "Each adult ticket cost $7.50.  Let's think about that:<BR>\n" );
document.write( "If they sold 1 adult ticket, they made <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2A1 ALIGN=MIDDLE  ALT=\"7.50%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "If they sold 2 adult tickets, they made <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2A2 ALIGN=MIDDLE  ALT=\"7.50%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "If they sold \"a\" adult tickets, they made <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2Aa ALIGN=MIDDLE  ALT=\"7.50%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Make sense?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2Aa%2B4.50%2Ac=540 ALIGN=MIDDLE  ALT=\"7.50%2Aa%2B4.50%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<hr />5.  Solve the equation.\r<BR>\n" );
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document.write( "We have 2 equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=80 ALIGN=MIDDLE  ALT=\"a%2Bc=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2Aa%2B4.50%2Ac=540 ALIGN=MIDDLE  ALT=\"7.50%2Aa%2B4.50%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You'll see this all the time in word problems:  2 equations, and 2 unknowns.  You'll definitely want to know how to solve these.  How?\r<BR>\n" );
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document.write( "Let's use substitution.  <BR>\n" );
document.write( "First, find the equation which looks simpler.  Do you see it?  The top equation looks simpler:  Neither one of the variables has coefficients (numbers) in front of them.  \r<BR>\n" );
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document.write( "Second, solve for one of the variables (get it alone).  It doesn't matter which one you choose.  I'll pick \"a\".  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=80 ALIGN=MIDDLE  ALT=\"a%2Bc=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=80-c ALIGN=MIDDLE  ALT=\"a=80-c\"   DISABLED_style= \"max-width:90%; height:auto;\" >	(subtracted \"c\" from both sides)<BR>\n" );
document.write( "(This says that \"a\" <i>is the same as</i> \"80-c\")\r<BR>\n" );
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document.write( "So, in our second equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2Aa%2B4.50%2Ac=540 ALIGN=MIDDLE  ALT=\"7.50%2Aa%2B4.50%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can substitute \"80-c\" for \"a\".  We get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2A%2880-c%29%2B4.50%2Ac=540 ALIGN=MIDDLE  ALT=\"7.50%2A%2880-c%29%2B4.50%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" > That's substitution!  Very cool.  Make sense?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600-7.50%2Ac%2B4.50%2Ac=540 ALIGN=MIDDLE  ALT=\"600-7.50%2Ac%2B4.50%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" > (distributed 7.50) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600-3%2Ac=540 ALIGN=MIDDLE  ALT=\"600-3%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" > (combined like terms, \"c\") <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Ac=-60 ALIGN=MIDDLE  ALT=\"-3%2Ac=-60\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracted 600 from both sides) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=20 ALIGN=MIDDLE  ALT=\"c=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > (divided both sides by -3) \r<BR>\n" );
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document.write( "So, the number of child tickets is 20.  If they sold 80 tickets total, there must have been 60 adult tickets.  Want proof?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=80 ALIGN=MIDDLE  ALT=\"a%2Bc=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B20=80 ALIGN=MIDDLE  ALT=\"a%2B20=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=60 ALIGN=MIDDLE  ALT=\"a=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracted 20 from both sides)\r<BR>\n" );
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document.write( "<hr />6.  Check your solution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2Aa%2B4.50%2Ac=540 ALIGN=MIDDLE  ALT=\"7.50%2Aa%2B4.50%2Ac=540\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.50%2A60%2B4.50%2A20=540 ALIGN=MIDDLE  ALT=\"7.50%2A60%2B4.50%2A20=540\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=450%2B90=540 ALIGN=MIDDLE  ALT=\"450%2B90=540\"   DISABLED_style= \"max-width:90%; height:auto;\" > Shazam!  It checks.\r<BR>\n" );
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document.write( "<hr />For more worked problems, or tutoring, please visit <a  rel=nofollow HREF=\"http://www.mathlocker.com\">MathLocker.com</a>. </SPAN>\n" );
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