Question 264461
Let x = the number of liters of the 60% solution. After changing the percentages to their decimal equivalents, we can write:
{{{x(0.6)+(100-x)(0.4) = 100(0.5)}}} Simplify and solve for x.
[{{0.6x+40-0.4x = 50}}} Subtract 40 from both sides and combine the x's.
{{{0.2x = 10}}} Divide both sides by 0.2
{{{highlight(x = 50)}}}
The chemist will need to mix 50 liters of the 60% solution with 40 (100-x) liters of the 40% solution to obtain 100 liters of 50% solution.