document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151454>Question 1151454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A solution containing a 9% concentration of acid is mixed with a solution containing a 5% concentration of acid to get 100mL of solution containing an 8% concentration of acid. How many mL of each solution is needed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773196 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=773196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's say we had two bottles of the acid.<BR>\n" );
document.write( "Bottle A has 9% concentration of acid.<BR>\n" );
document.write( "Bottle B has 5% concentration of acid.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We don't know how many mL of solution is in each bottle, so let,<BR>\n" );
document.write( "x = amount of solution in bottle A<BR>\n" );
document.write( "y = amount of solution in bottle B<BR>\n" );
document.write( "Each bottle contains pure acid plus other stuff (either water only or other chemicals as well).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We want to mix the two bottles (A and B) so that we end up with 100 mL of total solution. <BR>\n" );
document.write( "This means the amounts x and y must add to 100<BR>\n" );
document.write( "x+y = 100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve for y to get<BR>\n" );
document.write( "x+y = 100<BR>\n" );
document.write( "x+y-x = 100-x<BR>\n" );
document.write( "y = 100-x<BR>\n" );
document.write( "We will use this equation later. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From bottle A, we have 9% acid concentration. If we have x mL of solution in this bottle, then there is 0.09*x mL of pure acid here. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Inside bottle B is 0.05*y mL of pure acid because of the 5% concentration.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "All together, there is 0.09x+0.05y mL of pure acid. Let's call this quantity C. So C = 0.09x+0.05y\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We want to divide the value of C over 100 which was the total amount of solution we end up with when we mix the two bottles. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The expression C/100 is the percentage of pure acid in the final mixture. <BR>\n" );
document.write( "We want this percentage to be 8%\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So,<BR>\n" );
document.write( "C/100 = 0.08<BR>\n" );
document.write( "C = 100*0.08  ...... multiply both sides by 100<BR>\n" );
document.write( "C = 8<BR>\n" );
document.write( "0.09x+0.05y = 8 .... replace C with 0.09x+0.05y<BR>\n" );
document.write( "0.09x+0.05( y ) = 8<BR>\n" );
document.write( "0.09x+0.05( 100-x ) = 8 .... plug in y = 100-x<BR>\n" );
document.write( "0.09x+0.05(100)+0.05(-x) = 8 .... distribute<BR>\n" );
document.write( "0.09x+5-0.05x = 8<BR>\n" );
document.write( "0.04x+5 = 8 <BR>\n" );
document.write( "0.04x+5-5 = 8-5 ..... subtract 5 from both sides<BR>\n" );
document.write( "0.04x = 3<BR>\n" );
document.write( "0.04x/0.04 = 3/0.04 .... divide both sides by 0.04<BR>\n" );
document.write( "x = 75<BR>\n" );
document.write( "We will need 75 mL of the 9% concentration\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 100-x<BR>\n" );
document.write( "y = 100-75 .... plug in x = 75<BR>\n" );
document.write( "y = 25<BR>\n" );
document.write( "and we need 25 mL of the 5% concentration.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=red size=4>Answers: </font><BR>\n" );
document.write( "<font color=red size=4>75 mL</font> of the 9% concentration<BR>\n" );
document.write( "<font color=red size=4>25 mL</font> of the 5% concentration\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As a check,<BR>\n" );
document.write( "9% of 75 = 0.09*75 = 6.75 is the amount of pure acid from bottle A<BR>\n" );
document.write( "5% of 25 = 0.05*25 = 1.25 is the amount of pure acid from bottle B<BR>\n" );
document.write( "6.75+1.25 = 8 mL is the amount of pure acid in total after mixing both bottles<BR>\n" );
document.write( "100 mL is the total amount of solution<BR>\n" );
document.write( "8/100 = 0.08 = 8% is the proper concentration we're aiming for. <BR>\n" );
document.write( "This helps confirm the answer<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );