Expert: Paul Klarreich - 12/15/2010

Question
A 25% brine solution was mixed with a 18% brine solution to produce   a 20% brine solution. Determine how much of the 25% solution and how much of   the 18% solution were used to produce 28 gallons of the 20% solution. Enter the amount of the 25% solution in the answer box below.

Answer
Hi, Alicia.

I recently sent an answer to 'Megan' for a similar problem.  Here is what I wrote:

................................................................
Hi, Megan,

There are a whole class of problems that work the same way:

Rate-time-distance.
Mixture problems.
Percent solution problems.

-- and a few others.  Set up a little table.  (And PLEASE don't

ever call it a chart -- makes me throw up.)

OK, enough of that stuff.

Set it up like this:

(BTW, if the solution is 70% water, what is the other stuff?  Ok, I

won't ask.)

Kind of stuff        Number            Ltrs of
                   of ltrs. * Pct  =  Water
----------------------------------------------
70% solution        |       |        |       |
----------------------------------------------
90% solution        |       |        |       |
----------------------------------------------
85% mixture         |       |        |       |
----------------------------------------------

Now fill in information from the problem, deciding that

x = number of liters of 70% solution to add.

Kind of stuff        Number            Ltrs of
                   of ltrs. * Pct  =  Water
----------------------------------------------
70% solution        |   x   |  .7    |       |
----------------------------------------------
90% solution        |   6   |  .9    |       |
----------------------------------------------
85% mixture         |       |  .85   |       |
----------------------------------------------


Fill in more, such as the fact that the ltrs of water are the

result of multiplication:


Kind of stuff        Number            Ltrs of
                   of ltrs. * Pct  =  Water
----------------------------------------------
70% solution        |   x   |  .7    |  .7 x |
----------------------------------------------
90% solution        |   6   |  .9    | 5.4   |
----------------------------------------------
85% mixture         |       |  .85   |       |
----------------------------------------------

and that the numbers of liters must add up:

Kind of stuff        Number            Ltrs of
                   of ltrs. * Pct  =  Water
----------------------------------------------
70% solution        |   x   |  .7    |  .7 x |
----------------------------------------------
90% solution        |   6   |  .9    | 5.4   |
----------------------------------------------
85% mixture         |  x+6  |  .85   |  ???? |
----------------------------------------------

Now the key:  The ???? is the product across: .85(x+6).

But the ???? is also the sum:  .7x + 5.4

Got the clue, now?  Those are equal:

.7x + 5.4 = .85(x + 6)

You will solve that equation.  (Hint: clear the decimals first --

multiply all terms by 100.)

I will leave the rest to you.  My fingers are tired.
........................................

If this doesn't do it for you, send it again and I'll see what I can do.