document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=423344>Question 423344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if water is added in 80% wine then the wine become 60% . find the ratio of water is added to the wine<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 #295325 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=295325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your mixture is currently 80% wine.\r<BR>\n" );
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document.write( "that means it is 20% water.\r<BR>\n" );
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document.write( "let w equal the amount of water in the mixture.\r<BR>\n" );
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document.write( "let m = the amount of mixture.\r<BR>\n" );
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document.write( "currently w = .2 * m\r<BR>\n" );
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document.write( "that means the mixture is 20% water and 80% wine.\r<BR>\n" );
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document.write( "let y be equal to the amount of water you want to add to the mixture to make it 60% wine.\r<BR>\n" );
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document.write( "60% wine means 40% water.\r<BR>\n" );
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document.write( "your new formula will be:\r<BR>\n" );
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document.write( "(x + y) = .4 * (m + y)\r<BR>\n" );
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document.write( "since we know that x = .2 * m, we can substitute in this equation to get:\r<BR>\n" );
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document.write( "(.2 * m + y = .4 * (m + y)\r<BR>\n" );
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document.write( "removing parentheses, we get:\r<BR>\n" );
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document.write( ".2 * m + y = .4 * m + .4 * y\r<BR>\n" );
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document.write( "subtract .4 * y from both sides of this equation and subtract .2 * m from both sides of this equation to get:\r<BR>\n" );
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document.write( "y - (.4 * y) = (.4 * m) - (.2 * m)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".6 * y = .2 * m\r<BR>\n" );
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document.write( "divide both sides of this equation by .6 to get:\r<BR>\n" );
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document.write( "y = (.2/.6) * m\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y = .33333333 * m\r<BR>\n" );
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document.write( "in our equation of x + y = .4 * (m + y), we can substitute for x and y to get:\r<BR>\n" );
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document.write( "(.2 * m + .33333333 * m = .4 * (m + .333333333 * m)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( ".533333333333 * m = 1.33333333333 * m\r<BR>\n" );
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document.write( "the .53333333333 * m is the amount of water in the new mixture.\r<BR>\n" );
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document.write( "that represents .53333333333333 / 1.333333333333 * m which is equal to .4 * m which is the exact mixture that we want.\r<BR>\n" );
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document.write( "you start with x = .2 * m\r<BR>\n" );
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document.write( "you add y = .33333333333 * m.\r<BR>\n" );
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document.write( "The amount of water that is added to the original mixture is equal to 1/3 of the original mixture.\r<BR>\n" );
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document.write( "assume your original mixture was 12 gallons of water and 48 gallons of wine.\r<BR>\n" );
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document.write( "that's a total of 60 gallons of which 20% is water and 80% is wine.\r<BR>\n" );
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document.write( "you want to add 1/3 gallons * 60 of water to the mixture.\r<BR>\n" );
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document.write( "that's an additional 20 gallons of water.\r<BR>\n" );
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document.write( "the amount of water is now 32 gallons of water and the amount of wine is still 48 gallons for a total of 80 gallons of mixture.\r<BR>\n" );
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document.write( "32 / 80 = .4 = 40% of the mixture is water.<BR>\n" );
document.write( "48 / 80 = .6 = 60% of the mixture is wine.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "you add water equal to 1/3 of the original mixture to get 40% water and 60% wine in the new mixture.\r<BR>\n" );
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