document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74740>Question 74740</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780618503070/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A hair dye is made by blending a 7% hydrogen peroxide solution and a 4% hydrogen peroxide solution. How many milliliters of each are used to make a 300-millilter solution that is 5% hydrogen peroxide? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53718 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=53718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of 7% solution<BR>\n" );
document.write( "Then 300-x=amount of 4% solution\r<BR>\n" );
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document.write( "Now we know that the pure hydrogen peroxide that exists before things are mixed together must equal the amount of pure hydrogen peroxide that exists after things are mixed together.  So our equation to solve is:\r<BR>\n" );
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document.write( "0.07x+0.04(300-x)=0.05(300)  get rid of parens\r<BR>\n" );
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document.write( "0.07x+12-0.04x=15  subtract 12 from both sides\r<BR>\n" );
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document.write( "0.07x+12-12-0.04x=15-12  collect like terms\r<BR>\n" );
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document.write( "0.03x=3  divide both sides by 0.03\r<BR>\n" );
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document.write( "x=100 ml of 7% solution is needed\r<BR>\n" );
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document.write( "300-x=300-100=200 ml of 4% solution is needed\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "0.07(100)+0.04(300-100)=0.05(300)\r<BR>\n" );
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document.write( "7+8=15<BR>\n" );
document.write( "15=15\r<BR>\n" );
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document.write( "Another way to solve this problem would be:\r<BR>\n" );
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document.write( "Let x=amount of 7% solution<BR>\n" );
document.write( "Then y=amount of 4% solution\r<BR>\n" );
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document.write( "Now we are told that:\r<BR>\n" );
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document.write( "x+y=300----------------------------eq 1<BR>\n" );
document.write( "note: y=300-x\r<BR>\n" );
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document.write( "We are also told that<BR>\n" );
document.write( "0.07x+0.04y=0.05(300)--------------------eq 2  multiply eq 2 by 100\r<BR>\n" );
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document.write( "7x+4y=1500--------------eq2\r<BR>\n" );
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document.write( "substitute y=300-x from eq 1 into eq 2\r<BR>\n" );
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document.write( "7x+4(300-x)=1500  get rid of parens<BR>\n" );
document.write( "7x+1200-4x=1500  subtract 1200 from both sides<BR>\n" );
document.write( "3x=300  divide both sides by 3<BR>\n" );
document.write( "x=100 ml of 7%<BR>\n" );
document.write( "y=300-x=200 ml of 4%\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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