document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968792>Question 968792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi appreciated tutors,<BR>\n" );
document.write( "I have been studying linear systems and have a good understanding of solving them but this word problem is driving me crazy. Here is the problem verbatim;\r<BR>\n" );
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document.write( "The total cost of 10 gallons of regular gasoline and 15 gallons of premium gasoline is $32.75. Premium costs $.20 more per gallon than regular. What is the cost per gallon of each type of gasoline?\r<BR>\n" );
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document.write( "I tried to set up the problem like this:<BR>\n" );
document.write( "x+y=25<BR>\n" );
document.write( "10x+15y=32.75<BR>\n" );
document.write( "I figured the .20 would be added to the final \"y\" value. <BR>\n" );
document.write( "The way it comes out when I work the equations by trying to use substitution is a negative number. This is one indication I am working it incorrectly. Please show me a verbal model and work the equations and explain how to include the\".20\". THANKS very much!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591951 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "let the cost of regular gasoline be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the cost of premium gasoline be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D ALIGN=MIDDLE  ALT=\"p%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the total cost of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of regular gasoline and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of premium gasoline is $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32.75 ALIGN=MIDDLE  ALT=\"32.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10p%2B15p%5B1%5D=32.75 ALIGN=MIDDLE  ALT=\"10p%2B15p%5B1%5D=32.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1\r<BR>\n" );
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document.write( "if premium costs $.20 more per gallon than regular, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=p%2B0.20 ALIGN=MIDDLE  ALT=\"p%5B1%5D=p%2B0.20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The total cost is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10p%2B15%28p%2B0.20%29=32.75 ALIGN=MIDDLE  ALT=\"10p%2B15%28p%2B0.20%29=32.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10p%2B15p%2B3=32.75 ALIGN=MIDDLE  ALT=\"10p%2B15p%2B3=32.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25p=32.75-3 ALIGN=MIDDLE  ALT=\"25p=32.75-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=29.75%2F25 ALIGN=MIDDLE  ALT=\"p=29.75%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1.19 ALIGN=MIDDLE  ALT=\"p=1.19\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>the cost per gallon of regular gasoline\r<BR>\n" );
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document.write( "now find the price of premium\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=p%2B0.20 ALIGN=MIDDLE  ALT=\"p%5B1%5D=p%2B0.20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=1.19%2B0.20 ALIGN=MIDDLE  ALT=\"p%5B1%5D=1.19%2B0.20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B1%5D=1.39 ALIGN=MIDDLE  ALT=\"p%5B1%5D=1.39\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>the cost per gallon of premium gasoline\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "the total cost of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of regular gasoline is $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A1.19=11.9 ALIGN=MIDDLE  ALT=\"10%2A1.19=11.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > gallons of premium gasoline is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A1.39=20.85 ALIGN=MIDDLE  ALT=\"15%2A1.39=20.85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " then $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32.75=11.9%2B20.85 ALIGN=MIDDLE  ALT=\"32.75=11.9%2B20.85\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32.75=32.75 ALIGN=MIDDLE  ALT=\"32.75=32.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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