SOLUTION: 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
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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 Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52776) (Show Source):
Let x be the volume of the 3% elixir to mix / (to add), in milliliters.
Then you have this equation for the pure elixir amount before and after the mixing
0.03x + 0.09*10 = 0.05(x+10).
From the equation
x = = 20.
ANSWER. 20 mL.
CHECK. I will check the concentration = 0.05 = 5%. ! Precisely correct !
You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.
Read them and become an expert in solution mixture word problems.
You should know and understand the formal algebraic method for solving 2-part mixture problems like this, as shown by the other tutor.
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.
You are starting with a 9% solution and adding 3% solution to end up with a 5% solution.
Think of the problem like this:
(1) I'm starting at 9% and heading towards 3%, stopping when I get to 5%.
(2) 5% is 2/3 of the way from 9% to 3%. (picture the three percentages on a number line....)
(3) That means 2/3 of the mixture is the 3% solution that I am adding.
So the 10mL of 9% you started with is 1/3 of the final solution; that means the 2/3 you added is 20mL.
