document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107937>Question 107937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What amount of each mixture, one 95% alcohol and the other 15% alcohol, must be used to make 10 liters of a mixture which is 45% alcohol? what equation or equations will express this problem?  I was thinking it would be this equation: 0.95x+0.15x=0.45 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78680 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=78680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AT LEAST YOU GAVE IT A SHOT BUT YOU ARE GENERALLY FAR BETTER OFF IF YOU LAY OUT THE WORD PROBLEMS (WHAT EQUALS WHAT) AS I HAVE DONE BELOW.\r<BR>\n" );
document.write( "\n" );
document.write( "Let x=the amount of 95% alcohol mixture<BR>\n" );
document.write( "Then 10-x=amount of 15% alcohol mixture\r<BR>\n" );
document.write( "\n" );
document.write( "Now we know that the amount of pure alcohol in the 95% mixture (0.95x) plus the amount of pure alcohol in the 15% mixture (0.15(10-x)) has to equal the amount of pure alcohol in the 45% mixture (0.45*10).  So our equation to solve is:\r<BR>\n" );
document.write( "\n" );
document.write( "0.95x+0.15(10-x)=0.45*10 get rid of parens (distributive law)<BR>\n" );
document.write( "0.95x+1.5-0.15x=4.5   subtract 1.5 from both sides\r<BR>\n" );
document.write( "\n" );
document.write( "0.95x+1.5-1.5-0.15x=4.5-1.5  collect like terms\r<BR>\n" );
document.write( "\n" );
document.write( "0.80x=3  divide both sides by 0.80\r<BR>\n" );
document.write( "\n" );
document.write( "x=3.75 liters-----------amount of 95% alcohol mixture<BR>\n" );
document.write( "10-x=10-3.75= 6.25 liters-----------------amount of 15% alcohol mixture\r<BR>\n" );
document.write( "\n" );
document.write( "CK<BR>\n" );
document.write( "0.95*3.75+0.15*6.25=0.45*10<BR>\n" );
document.write( "3.5625+0.9375=4.5\r<BR>\n" );
document.write( "\n" );
document.write( "4.5=4.5\r<BR>\n" );
document.write( "\n" );
document.write( "ANOTHER WAY\r<BR>\n" );
document.write( "\n" );
document.write( "Let x=amount of 95% alcohol mixture<BR>\n" );
document.write( "And let y=amount of 15% alcohol mixture<BR>\n" );
document.write( "Now we are told that:\r<BR>\n" );
document.write( "\n" );
document.write( "x+y=10----------------------eq1<BR>\n" );
document.write( "We also know that:\r<BR>\n" );
document.write( "\n" );
document.write( "0.95x+0.15y=0.45*10------------------eq2\r<BR>\n" );
document.write( "\n" );
document.write( "From eq1, y=10-x.  Substitute this into eq2 and we get:\r<BR>\n" );
document.write( "\n" );
document.write( "0.95x+0.15(10-x)=4.5-----------------same equation as before.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps---ptaylor\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );