How many liters of 80% alcohol solution and 30% alcohol solution must be mixed to obtain 15 liters of 50% alcohol solution?

set up a table (multiply across and add down - don't add the middle column). Use the equation created by the "Total" row to solve for the variable.

               Quantity  (times)      %        equals        Total

Sol'n 1:          x            *           .80             =            (x)(.8)

Sol'n 2:      15 - x        *           .30             =          (15 - x)(.3)

Total:          15            *          .50              =          .8x + .3(15 - x)

                                15(.5)                        =         .8x + 4.5 - .3x

7.5 = .5x + 4.5

3.0 = .5x

6 = x

6 liters of 80% and 9 liters of 30%

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )