document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174670>Question 1174670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain car ideally requires an engine oil which is composed of 91.50% base oil and the rest in additives. How many gallons of 87.00% engine oil and how many gallons of 93.50% engine oil must be combined to produce 50.00 gallons of 91.50% engine oil? rounded up 2 decimals. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800120 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=800120\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the 87% oil.<BR>\n" );
document.write( "let y = the 93.5% oil.\r<BR>\n" );
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document.write( "x + y must be equal to 50.<BR>\n" );
document.write( "that's your first equation.\r<BR>\n" );
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document.write( ".87 * x + .935 * y must be equal to .915 * 50<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( ".87 * x + .935 * y = 45.75<BR>\n" );
document.write( "that's your second equation.\r<BR>\n" );
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document.write( "these two equations need to be solved simultaneously.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "x + y = 50<BR>\n" );
document.write( ".87 * x + .935 * y = 45.75\r<BR>\n" );
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document.write( "multiply both sides of your first equation  by .87 and leave your second equation as is to get:\r<BR>\n" );
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document.write( ".87 * x + .87 * y = .87 * 50<BR>\n" );
document.write( ".87 * x + .935 * y = 45.75\r<BR>\n" );
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document.write( "simplify the first equation and leave the second equation as is to get:\r<BR>\n" );
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document.write( ".87 * x + .87 * y = 43.5<BR>\n" );
document.write( ".87 * x + .935 * y = 45.75\r<BR>\n" );
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document.write( "subtract the first equation from the first to get;\r<BR>\n" );
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document.write( ".065 * y = 2.25\r<BR>\n" );
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document.write( "you have just reduced 2 equations with 2 unknowns to 1 equation with 1 unknown.\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 2.25 /.065 = 34.61538462.\r<BR>\n" );
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document.write( "since x + y = 50, then you get:\r<BR>\n" );
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document.write( "y = 34.61538462.<BR>\n" );
document.write( "x = 50 minus y = 15.38461538.\r<BR>\n" );
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document.write( "those values of x and y should be your answers.<BR>\n" );
document.write( "to confirm, replace x and y in the two original equations to get:\r<BR>\n" );
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document.write( "x + y = 50 becomes 34.61538462 + 15.38461538 which becomes 50 = 50 which is true.\r<BR>\n" );
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document.write( ".87 * x + .935 * y = 45.75 becomes .87 * 34.61538462 + .935 * 15.38461538 = 45.75 which becomes 45.75 = 45.75 which is true.\r<BR>\n" );
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document.write( "both equations are true with the values of x and y that were calculated by solving the simultaneous equations.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "your solution is that 34.62 gallons of 87% engine oil plus 15.38 gallons of 93.5%% engine oil get you 50 gallons of 91.5% engine oil.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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