document.write( "Question 1175881: How much of an elixir that is 3% medication should a pharmacist mix with 10mL of an elixir that is 9% medication to make an elixir that is 5% medication \n" ); document.write( "

Algebra.Com's Answer #801659 by greenestamps(13198) $\"\"$ $\"About$

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\n" ); document.write( "You should know and understand the formal algebraic method for solving 2-part mixture problems like this, as shown by the other tutor.

\n" ); document.write( "If a formal algebraic solution is not required, and if solving the problem as fast as possible is desired (as in a timed mathematics competition) here is a quick and easy way of solving any problem like this.

\n" ); document.write( "You are starting with a 9% solution and adding 3% solution to end up with a 5% solution.

\n" ); document.write( "Think of the problem like this:
\n" ); document.write( "(1) I'm starting at 9% and heading towards 3%, stopping when I get to 5%.
\n" ); document.write( "(2) 5% is 2/3 of the way from 9% to 3%. (picture the three percentages on a number line....)
\n" ); document.write( "(3) That means 2/3 of the mixture is the 3% solution that I am adding.

\n" ); document.write( "So the 10mL of 9% you started with is 1/3 of the final solution; that means the 2/3 you added is 20mL.

\n" ); document.write( "ANSWER: 20mL

\n" ); document.write( "CHECK:
\n" ); document.write( ".09(10)+.03(20) = .9+.6 = 1.5
\n" ); document.write( ".05(10+20) = .05(30) = 1.5

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