Question 1192851
<pre>
This is the way mixture problems are usually taught, using charts.

We're mixing a weaker solution and a stronger solution to get a
medium strength (final) solution.

Make this chart:

                  -------------------------------------------------
                  |   ounces   | % as decimal | oz. of pure alcohol
-------------------------------------------------------------------
weaker solution   |            |              |     
-------------------------------------------------------------------
stronger solution |            |              |    
===================================================================
medium strength   |            |              |
-------------------------------------------------------------------


Fill in the given percentages expressed as decimals, and the given
amount of the stronger solution:


                  -------------------------------------------------
                  |   ounces   | % as decimal | oz. of pure alcohol
-------------------------------------------------------------------
weaker solution   |            |      0.15    |     
-------------------------------------------------------------------
stronger solution |     8      |      0.20    |     
===================================================================
medium strength   |            |      0.19    |
-------------------------------------------------------------------

We want to know the number of ounces of the weaker solution, so we
put x there.


                  -------------------------------------------------
                  |   ounces   | % as decimal | oz. of pure alcohol
-------------------------------------------------------------------
weaker solution   |     x      |      0.15    |     
-------------------------------------------------------------------
stronger solution |     8      |      0.20    |     
===================================================================
medium strength   |            |      0.19    |
-------------------------------------------------------------------

We add the number of ounces of the weaker (x) and stronger solutions
(8) and that gives x+8 ounces of medium strength (final) solution.


                  -------------------------------------------------
                  |   ounces   | % as decimal | oz. of pure alcohol
-------------------------------------------------------------------
weaker solution   |     x      |      0.15    |    
-------------------------------------------------------------------
stronger solution |     8      |      0.20    |    
===================================================================
medium strength   |    x+8     |      0.19    |
-------------------------------------------------------------------

We multiply each of the ounces by the percentage expressed as a
decimal to get the ounces of pure alcohol contained in each solution:


                  -------------------------------------------------
                  |   ounces   | % as decimal | oz. of pure alcohol
-------------------------------------------------------------------
weaker solution   |     x      |      0.15    |     0.15x
-------------------------------------------------------------------
stronger solution |     8      |      0.20    |     0.20(8)
===================================================================
medium strength   |    x+8     |      0.19    |     0.19(x+8)
-------------------------------------------------------------------

The equation comes from the right column, the ounces of pure alcohol:

{{{0.15x + 0.20(8) = 0.19(x+8)}}}

Move the decimal 2 places right in each term:

{{{15x + 20(8) = 19(x+8)}}}

Solve that for x.

{{{15x + 160 = 19x + 152)}}}

{{{8 = 4x}}}

{{{2 = x}}}

2 ounces of the weaker 15% solution.

Edwin</pre>