SOLUTION: everett wishes to clean his boat with a 15%soap solution how much of a 10% soap solution and a 20% soap solution should he add to a quart of pure water to make a 30 qt of a 15% sol

From the condition, you have THESE two equations

   x +    y + 1 = 30,         (1)    (total volume)
0.1x + 0.2y     = 0.15*30.    (2)    (soap contents)


Simplify both equations:

   x +    y = 29,             (3)  
  1x +   2y = 45.             (4)   


Now subtract eq(3) from eq(4). You will get

y = 45 - 29 = 16 .

Then from eq(1),  x = 29-16 = 13.


Answer.  13 quart of the 10% soap solution plus 16 quart of the 20% soap solution plus one quart of pure water.


Check.  0.1*13 + 0.2*16 = 4.5;  

        0.15*3          = 4.5.    ! Correct !