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How many fluid ounces of a 60 percent saline solution must be mixed with a 75 percent saline solution to get 100 fluid ounces of a 72 percent solution?

There are four possible answers:
a. 15 fluid ounces.
b. 20 fluid ounces.
c. 24 fluid ounces.
d. 30 fluid ounces
Word problems like these confuse me and I just don't know where to put what. Help is appreciated!
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3 Answers

We want to mix 2 solutions - a 60%(.6) and a 75%(.75) saline solution to get a target solution.
Our target solution = 100 fluid oz, 72%(.72)concentration.
Let the Fluid ounces of the 60% solution = x        ( Note: Always equate what you are looking for to x.)
Therefore, .................the 75%  solution = 100-x ( This follows because our mixture of the two solutions is 100)
.60x + .75(100-x) = .72(100)
.60x + 75 - .75x = 72
.15x = 3
x = 3/.15  = 20.
Thanks Amy,
I've never thought of it that way before and I can certainly say you've taught both Grace and I a clever method to approach such type of problems.


You are quite welcome. This is a common pharmacy calculation. It's the method used when we are preparing a concentration of a liquid or solid medication that is unavailable commercially.  We use concentrations that are available and mix/dilute them to the needed strength.   It's a very clever and easy way to calculate 2 unknowns. 
The answer is 20 ounces. It can be solved by using alligation method.  This is used when you want to make a solution, cream, etc. of a particular concentration by using ingredients with different concentrations. 
      75     |       | 12
    _____ | ___ | _____
              |       |
              |  72  |
    _____ | ___ | _____
              |       |
         60 |       |   3
You set up a tic tac toe grid (#hashtag).  Put the concentration you are trying to make in the middle.  On the left hand side, put the two concentrations you have on hand in the top and bottom squares.  Then subtract on the diagonal, disregarding any negative numbers, and place those results in the respective boxes on the right hand of the grid
75 - 72 = 3
72 - 60 = 12
Now add the two numbers on the right hand side.   12 + 3 = 15
To find out how much of the 60% you need, you find 60 in the left hand box, go straight across to the number in the right hand box.  In this case, that number is 3.  
The equation is 3/15 * amount of solution you are trying to make   3/15 * 100 = 20 ounces