document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171918>Question 1171918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bob bought a popcorn, a soda, and a hotdog at the movies for $6.94. Popcorn costs $1 more than a hotdog. A soda costs $0.81 less than a hotdog. How much is each item? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796819 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = price of a box of popcorn<BR>\n" );
document.write( "s = price of one soda<BR>\n" );
document.write( "h = price of one hotdog<BR>\n" );
document.write( "t = total price\r<BR>\n" );
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document.write( "your equation is:<BR>\n" );
document.write( "t = p + s + h\r<BR>\n" );
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document.write( "you are given that the price of a box of popcorn is 1 dollar more than the price of a hotdog.<BR>\n" );
document.write( "the equation for that is:<BR>\n" );
document.write( "p = h + 1\r<BR>\n" );
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document.write( "you are given that the price of a soda is .81 less than the price of a hotdog.<BR>\n" );
document.write( "the equation for that is:<BR>\n" );
document.write( "s = h - .81\r<BR>\n" );
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document.write( "the equations you have so far are:<BR>\n" );
document.write( "t = p + s + h<BR>\n" );
document.write( "p = h + 1<BR>\n" );
document.write( "s = h - .81\r<BR>\n" );
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document.write( "what you want to do is reduce the number of unknowns in the equation of t = p + s + h down to 1.<BR>\n" );
document.write( "then you can solve for that one unknown.<BR>\n" );
document.write( "once you have that, you can use that value to solve for the rest of the unknowns.\r<BR>\n" );
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document.write( "looking at p = h + 1 and s = h - .81, it looks like h is in both of them.\r<BR>\n" );
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document.write( "we should be able to solve for p and s in terms of h.\r<BR>\n" );
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document.write( "we have p = h + 1 so we don't have to do anything with that because p is already solved for in terms of h.\r<BR>\n" );
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document.write( "we have s = h - .81 so we don't have to do anything with that because s is already solved for in terms of h.\r<BR>\n" );
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document.write( "in the equation of t = p + s + h, replace p with h + 1 and replace s with h - .81 to get:\r<BR>\n" );
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document.write( "t = p + s + h becomes:<BR>\n" );
document.write( "t = (h + 1) + (h - .81) + h<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "t = h + 1 + h - .81 + h<BR>\n" );
document.write( "regroup the terms so that like terms are grouped together to get:<BR>\n" );
document.write( "t = (h + h + h) + (1 - .81).<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "t = 3h + .19\r<BR>\n" );
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document.write( "since t = 6.94, the equation becomes:<BR>\n" );
document.write( "6.94 = 3h + .19<BR>\n" );
document.write( "subtract .19 from both sides of the equation to get:<BR>\n" );
document.write( "6.94 - .19 = 3h<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "6.75 = 3h<BR>\n" );
document.write( "solve for h to get:<BR>\n" );
document.write( "h = 6.75 / 3 = 2.25\r<BR>\n" );
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document.write( "from s = h - .81, you get s = 2.25 - .81 which becomes:<BR>\n" );
document.write( "s = 1.44\r<BR>\n" );
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document.write( "from p = h + 1, you get p = 2.25 + 1 which becomes:<BR>\n" );
document.write( "p = 3.25\r<BR>\n" );
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document.write( "you now have:<BR>\n" );
document.write( "p = 3.25<BR>\n" );
document.write( "s = 1.44<BR>\n" );
document.write( "h = 2.25\r<BR>\n" );
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document.write( "t = p + s + h becomes:<BR>\n" );
document.write( "t = 3.25 + 1.44 + 2.25 = 6.94<BR>\n" );
document.write( "this agrees with t is supposed to be, so the numbers for p and s and h look good.\r<BR>\n" );
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document.write( "your solution is that the price of a box of popcorn is 3.25 and the price of a soda is 1.44 and the price of a hotdog is 2.25.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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