A pharmacist needs 40 liters of a 50% alcohol solution. He has 30% and an 80% alcohol solution. How many liters of each will be required to make 40 liters of a 50% solution?
30x + 80(40-x) = 50*40
To solve the problem, we can set up a system of equations based on the given information.
Let's assume that the pharmacist will need x liters of the 30% alcohol solution and (40 - x) liters of the 80% alcohol solution to make a total of 40 liters of the 50% alcohol solution.
Now we can write the equation for the total amount of alcohol in the mixture:
0.30x + 0.80(40 - x) = 0.50(40)
Simplifying the equation, we have:
0.30x + 32 - 0.80x = 20
Combining like terms, we get:
-0.50x = -12
To isolate x, divide both sides of the equation by -0.50:
x = -12 / -0.50
x = 24
Therefore, the pharmacist will need 24 liters of the 30% alcohol solution and (40 - 24) = 16 liters of the 80% alcohol solution to make 40 liters of the 50% alcohol solution.