document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768490>Question 768490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello. I work for a veterinarian that likes to mix solutions using injectable medications. He likes to make diluted solutions as he uses very small doses. I will give an example as I understand what he wants but cannot fully understand the mathematics behind making the solution.<BR>\n" );
document.write( "I have a medication X that is concentrated at 25mg/ml. <BR>\n" );
document.write( "I want to make up a solution to dilute this to 0.05mg/ml with a target volume of 4ml.<BR>\n" );
document.write( "How much of medication X needs to be mixed with how much sterile saline (which will just dilute it, that's all) to make the total of 4ml.<BR>\n" );
document.write( "It is the math to figure out how much of medication X that I need. Also, I cannot figure out if the target volume has any effect on the calculations.<BR>\n" );
document.write( "Please help! I want to understand this!<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468309 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have a medication X that is concentrated at 25mg/ml. <BR>\n" );
document.write( "I want to make up a solution to dilute this to 0.05mg/ml with a target volume of 4ml.<BR>\n" );
document.write( "How much of medication X needs to be mixed with how much sterile saline (which will just dilute it, that's all) to make the total of 4ml.<BR>\n" );
document.write( "It is the math to figure out how much of medication X that I need. Also, I cannot figure out if the target volume has any effect on the calculations.<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( "I have a medication X that is concentrated at 25mg/ml. <BR>\n" );
document.write( "I want to make up a solution to dilute this to 0.05mg/ml with a target volume of 4ml.<BR>\n" );
document.write( "How much of medication X needs to be mixed with how much sterile saline (which will just dilute it, that's all) to make the total of 4ml.<BR>\n" );
document.write( "t = amount of 25 mg/ml<BR>\n" );
document.write( "s = amount of saline<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t + s = 4  (total solution)<BR>\n" );
document.write( "25t + 0*s = 0.05*(t+s) (total medication)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t + s = 4  --> s = 4-t<BR>\n" );
document.write( "25t + 0*s = 0.05*(t+s)<BR>\n" );
document.write( "Sub for s<BR>\n" );
document.write( "25t = 0.05*(t + 4-t)<BR>\n" );
document.write( "25t = 0.05*4 = 0.2<BR>\n" );
document.write( "t = 0.2/25<BR>\n" );
document.write( "t = 0.008 ml of the 25 mg/ml<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "That's how mixing 2 solutions is done.<BR>\n" );
document.write( "Straight dilution is simpler.  Diluting from 25 to 0.05 is 1/500.<BR>\n" );
document.write( "For 4 ml of 0.05 you need 4/500 ml of the original = 0.008 ml<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "That's not much, might be hard to measure.<BR>\n" );
document.write( "It takes very little because it's being diluted to 1/500 of its concentration.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );