document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=795155>Question 795155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hector is performing an experiment that requires 160 ml of 40% sulfuric solution.  He has a 25% sulfuric acid solution and a 50% sulfuric acid solution.  How many ml of each solution should he mix to obtain the needed solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #480827 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=480827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set up two equations, much like you do for coin problems. One for the value and one for the number of coins. On;y now you use liquids with a different percentage concentration and you have the total volume of the combined concentrations.<BR>\n" );
document.write( "Let a = the number of milliliters of the 25% sulfuric acid solution<BR>\n" );
document.write( "Let b = the number of milliliters of the 50% sulfuric acid solution<BR>\n" );
document.write( "Let c = the number of milliliters of the total 40% sulfuric acid solution<BR>\n" );
document.write( "Using the volume we have<BR>\n" );
document.write( "(1) a + b = c or<BR>\n" );
document.write( "(2) a + b = 160<BR>\n" );
document.write( "Now for the mixture we have<BR>\n" );
document.write( "(3) .25*a + .5*b = .4*c or<BR>\n" );
document.write( "(4) a/4 + b/2 = .4*160 or<BR>\n" );
document.write( "(5) a/4 + b/2 = 64 or <BR>\n" );
document.write( "(6) a + 2*b = 4*64 or<BR>\n" );
document.write( "(7) a + 2*b = 256 <BR>\n" );
document.write( "Now solve (7) and (2) simultaneously to get a and b.<BR>\n" );
document.write( "The first step is to subtract (2) from (7) to get<BR>\n" );
document.write( "(8) (a + 2*b) - (a + b) = 256 - 160 or<BR>\n" );
document.write( "(9) a - a + 2*b - b = 96 or<BR>\n" );
document.write( "(10) b = 96<BR>\n" );
document.write( "Then from (2) we get<BR>\n" );
document.write( "(11) a + 96 = 160 or<BR>\n" );
document.write( "(12) a = 160 - 96 or<BR>\n" );
document.write( "(13) a = 64<BR>\n" );
document.write( "Let's (always) check our answer with (3).<BR>\n" );
document.write( "Is (.25*64 + .5*96 = .4*160)?<BR>\n" );
document.write( "Is (16 + 48 = 64)?<BR>\n" );
document.write( "Is (64 = 64)? Yes<BR>\n" );
document.write( "Answer: Hector should mix 64ml of the 25% solution with 96ml of the 50% solution in order to get 160ml at a 40% concentration of sulfuric acid.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );