Question 507045
Let x = the required number of liters of the 25% acid solution, then (10-x) is the required number of liters of the 50% acid solution.  These are mixed to obtain 10 liters (x+(10-x)) of 40% acid solution.  Let's write the equation to solve for x after changing the percentages to their decimal equivalents.
0.25x+0.5(10-x) = 0.4(10) Simplify.
0.25x+5-0.5x = 4 Combine the x-terms.
-0.25x+5 = 4 Subtract 5 from both sides.
-0.25x = -1 Finally, divide both sides by -0.25
x = 4 and 10-x = 6, so...
The chemist will need to mix 4 liters of the 25% acid solution with 6 liters of the 50% acid solution to obtain 10 liters of 40% acid solution.