document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1024640>Question 1024640</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many ounces of a 45% alcohol solution must be mixed with 18 ounces of a 50% alcohol solution to make a 46% alcohol&#8203; solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640021 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=640021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of ounces of the 45% solution.<BR>\n" );
document.write( "let y = the number of ounces of the 46% solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your formula is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + .50 * 18 = .46 * y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have another formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that formula is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + 18 = y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first formula is telling you the amount of alcohol.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the second formula is telling you the amount of solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these equations need to be solved simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means the same solution applies to both.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + .50 * 18 = .46 * y<BR>\n" );
document.write( "x + 18 = y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first equation can be simplified to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + 9 = .46 * y<BR>\n" );
document.write( "x + 18 = y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can replace y in the first equation with the equivalent value of y from the second equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + 9 = .46 * (x + 18).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + 9 = .46 * x + .46 * 18.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify further to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + 9 = .46 * x + 8.28.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract .45 * x from both sides of the equation and subtract 8.28 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9 - 8.28 = .46 * x - .45 * x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".72 = .01 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by .01 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".72 / .01 = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 72.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go back to your original equations and replace x with 72.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your original equations are, after they have been simplified:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * x + 9 = .46 * y<BR>\n" );
document.write( "x + 18 = y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with 72 and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".45 * 72 + 9 = .46 * y<BR>\n" );
document.write( "72 + 18 = y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the second equation, you get y = 90.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for y in the first equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = (.45 * 72 + 9) / .46 = 90.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 72<BR>\n" );
document.write( "y = 90\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x = the number of ounces of the 45% solution = 72.<BR>\n" );
document.write( "let y = the number of ounces of the 46% solution = 90.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you were asked for how many ounces of the 45% solution were required.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the answer is 72.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );