Question 209549
Let x = the number of liters of 25% acid solution required and this is to be mixed with (10-x) liters of 50% acid solution to obtain 10 liters of 40% acid solution.
The key here is to set up an equation showing the quantities of acid.
The quantity of acid in the x liters of the 25% acid solution can be expressed by: 25%(x) and the quantity of acid in the (10-x) liters of the 50% acid solution can be expressed by: 50%(10-x).  When mixed together, these will produce 10 liters of 40% acid solution which is 40%(10) acid. So, after converting the percentages to their decimal quivalents, we can write the equation:
0.25(x)+0.5(10-x) = 0.4(10) Simplify and solve for x.
0.25x+5-0.5x = 4 Combine the x-terms.
-0.25x+5 = 4 Subtract 5 from both sides.
-0.25x = -1 Divide both sides by -0.25
x = 4
The chemist willl need to mix 4 liters of 25% acid solution with 6 liters (from 10-x) of 50% acid solution to obtain 10 liters of 40% acid solution.