document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204426>Question 1204426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given 98% gasoline and 2% motor oil. New engine is  96% gasoline and 4% oil. write an equation in standard form that ma<BR>\n" );
document.write( "kes the possible combination of each kind of mixture you can  prepare using 6 gallons of gasoline. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840676 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=840676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> number of galons of gas = 6<BR>\n" );
document.write( "number of gallons of oil = x<BR>\n" );
document.write( "ratio of gas to total = y\r<BR>\n" );
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document.write( "i get x = 6/y - 6\r<BR>\n" );
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document.write( "when y = .98, the equation becomes x = 6/.98 - 6 which gets you x = .1224489796.\r<BR>\n" );
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document.write( "when y = .96, the equation becomes x = 6/96 - 6 which gets you x = .25.\r<BR>\n" );
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document.write( "if 6 gallons of gas is 98% of the total, then the number of gallons of oil is equal to .1224489796.\r<BR>\n" );
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document.write( "if 6 gallons of gas is 96% of the total, then the number of gallons of oil is equal to .25.\r<BR>\n" );
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document.write( "at 98% gas, the total is 6.1224489796 gallons.<BR>\n" );
document.write( "6 divided by that = .98<BR>\n" );
document.write( ".12244489796 divided by that = .02\r<BR>\n" );
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document.write( "at 6% gas, the total is 6.25 gallons.<BR>\n" );
document.write( "6 divided by that = .96<BR>\n" );
document.write( ".25 divided by that = .04\r<BR>\n" );
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document.write( "the general equation for the number of gallons of oil required if you have 6 gallons of gas is x = 6/y - 6.<BR>\n" );
document.write( "x is the number of gallons of oil required.<BR>\n" );
document.write( "y is the ratio of gallons of gas to the total mixture.\r<BR>\n" );
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document.write( "the total mixture is expressed as 6/y.<BR>\n" );
document.write( "x is the nmber of gallons of oil required.<BR>\n" );
document.write( "the total mixture is expresed by the equation 6/y = 6 + x.<BR>\n" );
document.write( "y is the ratio of gallons of gas to total gallons of mixture.<BR>\n" );
document.write( "x is the number of gallons of oil reuired.<BR>\n" );
document.write( "since x = 6/y - 6, you can replace x with that to get:<BR>\n" );
document.write( "6/y = 6 + 6/y - 6<BR>\n" );
document.write( "you wind up with 6/y = 6/y which is correct.\r<BR>\n" );
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document.write( "what i wind up with is:<BR>\n" );
document.write( "standard form equation is 6y + xy = 6<BR>\n" );
document.write( "x is the number of gallons of oil required.<BR>\n" );
document.write( "y is the ratio of gallons of gas to total number of gallons.\r<BR>\n" );
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document.write( "it's a litle complex, but it works.\r<BR>\n" );
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document.write( "when y = .98, the equation becomes 6 * .98 + x * .98 =  6<BR>\n" );
document.write( "simplify to get 5.88 + .98 * x = 6<BR>\n" );
document.write( "subtract 5.88 from both sides of the equation to get .98 * x = .12<BR>\n" );
document.write( "solve for x to get x = .12 /.98 = .1224489796.<BR>\n" );
document.write( "this  is the correct answer as we derived above when 6 = .98 of the total mixture.\r<BR>\n" );
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document.write( "when y = .96, the equataion becomes 6 * .96 + x * .96 = 6<BR>\n" );
document.write( "simplify to get 5.76 + .96 * x = 6<BR>\n" );
document.write( "subtract 5.76 from both sides of the equation to get .96 * x = .24<BR>\n" );
document.write( "solve for x to get x = .24 / .96 = .25.<BR>\n" );
document.write( "this is the correct answer as we derived above when y = .96 of the total mixture.\r<BR>\n" );
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document.write( "it's important to know exactly what x and y represent.<BR>\n" );
document.write( "the equation is 6 * y + x * y = 6<BR>\n" );
document.write( "y is the ratio of gallons of gas to total gallons of mixture.<BR>\n" );
document.write( "x is the number of gallons of gas.\r<BR>\n" );
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document.write( "with this equation, you can figure out how many gallons of oil you need to make any mixture with 6 gallons of gas.<BR>\n" );
document.write( "all you need to do is provide the ratio of gallons gas to total gallons of mixture.\r<BR>\n" );
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