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

Answer: 6 liters of 80% and 9 liters of 30%