document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133340>Question 1133340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chef needs 6 L of a solution that is 70% sugar. He has a 30% sugar mixture and an 80% sugar mixture that he can combine to make the 70% mixture.\r<BR>\n" );
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document.write( "Let x represent the number of liters of the 30% sugar mixture and let y represent the number of liters of the 80% sugar mixture.\r<BR>\n" );
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document.write( "How many liters of each solution will he use?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750541 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=750541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 30% solution<BR>\n" );
document.write( "y = 80% solution.\r<BR>\n" );
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document.write( "you want 6 liters of a 70% solution.\r<BR>\n" );
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document.write( "first equation is x + y = 6\r<BR>\n" );
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document.write( "second equation is .3 * x + .8 * y = .7 * (x + y)\r<BR>\n" );
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document.write( "in the first equation solve for y to get y = 6 - x\r<BR>\n" );
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document.write( "in the second equation replace y with 6 - x to get:\r<BR>\n" );
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document.write( ".3 * x + .8 * y = .7 * (x + y) becomes .3 * x + .8 * (6 - x) = .7 * (x + 6 - x)\r<BR>\n" );
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document.write( "simplify to get .3 * x + 4.8 - .8 * x = 4.2\r<BR>\n" );
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document.write( "combine like terms to get: -.5 * x + 4.8 = 4.2\r<BR>\n" );
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document.write( "subtract 4.8 from both sides of this equation to get -.5 * x = -.6\r<BR>\n" );
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document.write( "divide both sides of this equation by -.5 to get:\r<BR>\n" );
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document.write( "x = -.6/-.5 = 1.2\r<BR>\n" );
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document.write( "in the equation of x + y = 6, replace x with 1.2 and solve for y to get:\r<BR>\n" );
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document.write( "y = 6 - 1.2 = 4.8\r<BR>\n" );
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document.write( "x + y = 6 becomes 1.2 + 4.8 = 6 which becomes 6 = 6 which is true.\r<BR>\n" );
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document.write( ".3 * x + .8 * y = .7 * (x + y) becomes .3 * 1.2 + .8 * 4.8 = .7 * (1.2 + 4.8) which becomes .36 + 3.84 = .7 * 6 which becomes 4.2 = 4.2 which is true.\r<BR>\n" );
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document.write( "the solution looks good.\r<BR>\n" );
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document.write( "x = 1.2 and y = 4.8\r<BR>\n" );
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document.write( "x + y = 6 becomes 1.2 + 4.8 = 6 which is true.\r<BR>\n" );
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document.write( ".3 * x + .8 * y becomes .3 * 1.2 + .8 * 4.8 which becomes .36 + 3.84 which becomes 4.2\r<BR>\n" );
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document.write( "4.2 / 6 = .7 = 70% which satisfies the requirements of the problem.\r<BR>\n" );
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document.write( "1.2 liters of a 30% mixture added to 4.8 liters of an 80% mixture results in 6 liters of a 70% solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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