Question 495507
Let x = the required number of liters of solution A (50% alcohol solution), then (20-x) will be the number of liters of solution B (20% alcohol solution).
The sum of these is to be 20 liters of 32% alcohol solution.
This situation can be expressed (after changing the percentages to their decimal equivalents) in the following equation:
{{{0.5x+0.20(20-x) = 0.32(20)}}} Simplify and solve for x.
{{{0.5x+4-0.2x = 6.4}}} Combine the x-terms.
{{{0.3x+4 = 6.4}}} Subtract 4 from both sides.
{{{0.3x = 2.4}}} Finally, divide both sides by 0.3
{{{x = 8}}}liters and...
{{{20-x = 12}}}liters.
You will need to mix 8 liters of solution A (the 50% alcohol solution) with 12 liters of solution B (the 20% alcohol solution) to obtain 20 liters of 32% alcohol solution.