document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926006>Question 926006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I  dilute a 70% peroxide solution to a 35%  solution then to a 3.5% solution<BR>\n" );
document.write( "using 250 ml of the 70% solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561928 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=561928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> basically you want to know how much water to add to the solution to dilute it enough so that you have a 35% solution and then dilute it again until you get a 3.5% solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you start with 70% of 250 ml = 175 ml of peroxide in the original solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you divide the amount of peroxide in the solution by the ratio of peroxide in the total solution, then you can derive the total solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 / .7 = 250.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can do the same for the new percentages under the assumption that the amount of peroxide will remain the same in all solutions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 / .35 = 500\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 / .035 = 5000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the original solution, the amount of water is equal to 75 ml because 250 - 175 = 75.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the 35% solution, the amount of water is equal to 325 ml because 500 - 175 = 325.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the 3.5% solution, the amount of water is equal to 4825 ml because 5000 - 175 = 4825.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's how it works out.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you start with 175 ml of peroxide and 75 ml of water to get a total of 250 ml of solution.<BR>\n" );
document.write( "175 / 250 = .7 * 100% = 70% peroxide solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you add 250 ml of water to get 175 ml of peroxide and 325 ml of water to get a total of 500 ml of solution.<BR>\n" );
document.write( "175 / 500 = .35 * 100% = 35% peroxide solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now you add 4500 ml of water to get 175 ml of peroxide plus 4825 ml of water to get a total of 5000 ml of solution.<BR>\n" );
document.write( "175 / 5000 = .035 * 100% = 3.5% peroxide solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be solved algebraically as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with .70 * 250 + .3 * 250 = 250\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is a 70% solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you want a 35% solution, then the amount of water in the solution will be equal to 65% because 100% - 35% = 65%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".70 * 250 + .65 * (250 + x) = 250 + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since .70 * 250 will stay  the same in all equations, we'll simplify that to 175.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 + .65 * (250 + x) = 250 + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we want to solve for x which tells us how much water to add to the solution to get a 35% solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in other words, x represents the amount of water to add to the solution.\r<BR>\n" );
document.write( "<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( "175 + .65 * 250 + .65 * x = 250 + x\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( "175 + 162.5 + .65 * x = 250 + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 250 from both sides of the equation and subtract .65 * x from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 + 162.5 - 250 = x - .65 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "87.5 = .35 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by .35 and solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 87.5 / .35 = 250.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you add 250 ml of water to the original 70% solution of 250 ml to get a 35% solution of 500 ml.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the 5.5% solution, a similar equation is applied.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation to start with is now:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 + .65 * 500 = 500 ml of a 35% peroxide solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you want to make it a 3.5% solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you have 3.5% of peroxide, then the rest of the solution must be 96.5% water.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 + .965 * (500 + x) = 500 + x\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( "175 + .965 * 500 + .965 * x = 500 + x\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( "175 + 482.5 + .965 * x = 500 + x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 500 from both sides of this equation and subtract .965 * x from both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "175 + 482.5 - 500 = x - .965 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "157.5 = .035 * x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by .035 and solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 4500\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you add 4500 ml of water to the original 35% solution of 500 ml to get a 3.5% solution of 5000 ml.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<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" );