document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=495151>Question 495151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this mixture word problem:<BR>\n" );
document.write( "A certain mixture consists of acid and water. If 5 gallons of acid is added to the mixture, it willl produce a mixture that is one-half acid and one-half water. If, on the other hand, 5 gallons of water is added, the resulting mixture is one-third acid. How many gallons of acid does the original mixture contain? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #336049 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=336049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A certain mixture consists of acid and water.<BR>\n" );
document.write( " If 5 gallons of acid is added to the mixture, it will produce a mixture that is one-half acid and one-half water.<BR>\n" );
document.write( " If, on the other hand, 5 gallons of water is added, the resulting mixture is one-third acid.<BR>\n" );
document.write( " How many gallons of acid does the original mixture contain?<BR>\n" );
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document.write( "Let x = the decimal value of of the percent acid in the original mixture<BR>\n" );
document.write( "Let y = the amt (in gallons of the original mixture)<BR>\n" );
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document.write( "write an equation for each statement, based on the amt of acid:<BR>\n" );
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document.write( "\"If 5 gallons of acid is added to the mixture, it will produce a mixture that is one-half acid and one-half water.\"<BR>\n" );
document.write( "xy + 5 = .5(y+5)<BR>\n" );
document.write( "xy + 5 = .5y + 2.5<BR>\n" );
document.write( "xy = .5y + 2.5 - 5<BR>\n" );
document.write( "xy = .5y - 2.5<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28.5y-2.5%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28%28.5y-2.5%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "\"If, on the other hand, 5 gallons of water is added, the resulting mixture is one-third acid.\"<BR>\n" );
document.write( "xy = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >(y+5)<BR>\n" );
document.write( "3xy = y + 5<BR>\n" );
document.write( "replace x with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28.5y-2.5%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28%28.5y-2.5%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >; find y<BR>\n" );
document.write( "3y(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28.5y-2.5%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28%28.5y-2.5%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = y + 5<BR>\n" );
document.write( "y cancels (fortunately) so we have<BR>\n" );
document.write( "3(.5y - 2.5) = y + 5<BR>\n" );
document.write( "1.5y - 7.5 = y + 5<BR>\n" );
document.write( "1.5y - y = 5 + 7.5<BR>\n" );
document.write( ".5y = 12.5<BR>\n" );
document.write( "multiply both side by 2<BR>\n" );
document.write( "y = 25 gal is the amt of the original mixture<BR>\n" );
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document.write( "Find x using x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28.5y-2.5%29%29%2Fy ALIGN=MIDDLE  ALT=\"%28%28.5y-2.5%29%29%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28.5%2825%29-2.5%29%29%2F25 ALIGN=MIDDLE  ALT=\"%28%28.5%2825%29-2.5%29%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2812.5-2.5%29%29%2F25 ALIGN=MIDDLE  ALT=\"%28%2812.5-2.5%29%29%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F25 ALIGN=MIDDLE  ALT=\"10%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = .4, the original mixture was 40% acid<BR>\n" );
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document.write( "See if that checks out in the first statement<BR>\n" );
document.write( "If 5 gallons of acid is added to the mixture, it will produce a mixture that is one-half acid and one-half water.\"<BR>\n" );
document.write( ".4(25) + 5 = .5(25 + 5)<BR>\n" );
document.write( "10 + 5 = .5(30); confirms our solution<BR>\n" );
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document.write( "An interesting problem (Most of them aren't)<BR>\n" );
document.write( "Did all this make sense to you? Make an effort to understand each step, ask me in the comment section, if you have a question.  C<BR>\n" );
document.write( " </SPAN>\n" );
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