SOLUTION: I really don't understand word problems, would you please help me with this problem? A researcher orders a broth of 8% glucose for her lab. However, she needs a stronger broth,o

What she has are two containers each containing some glucose
mixed with water, One is too strong and the other is too weak,
so she wants to add enough of the weak to all of the strong 
to dilute it down to the medium strength that she wants.

Let the amount of the weak that she needs to add to the strong 
be x liters.

We make this chart:
      
         liters of liquid | strength | liters of pure glucose in the liquid 
---------------------------------------------------------------------------
strong                    |          |
weak                      |          |          
medium                    |          |

We have 70.6 liters of liquid of the strong and we add x liters of
liquid of the weak so we will end up with (70.6 + x) liters of the
medium strength we want.

So we fill in the first column, which is the number of liters of liquid
of the strong and of the weak, and the final amout of liquid of medium
strength that we want to end up with.  We also fill in the middle
column with the three strengths.   

         liters of liquid | strength | liters of pure glucose in the liquid
---------------------------------------------------------------------------
strong           70.6     |    41%   |           
weak               x      |     8%   |             
medium         70.6 + x   |   14.1%  |         

Then we fill in the liters of pure glucose contained in each 


         liters of liquid | strength | liters of pure glucose in the liquid
---------------------------------------------------------------------------
strong           70.6     |    41%   |            .41(70.6)  
weak               x      |     8%   |             .08x  
medium         70.6 + x   |   14.1%  |         .141(70.6 + x)


Liters of pure        Liters of pure       Liters of pure
glucose in the    +   glucose in the   =   glucose in the   
   strong                 weak                 medium

              .41(70.6) + .08x = .141(70.6 + x)

Solve that and get x = 53.8527541 liters of weak that she needs to 
add to the strong solution to dilute it down to the medium strength she
wants.                  

Edwin