Let:
x = liters of the 35% acid solution
y = liters of the 85% acid solution
We can set up a system of equations based on the given information:
Total Volume: The total volume of the resulting solution is 80 liters.
x + y = 80 (liters)
Acid Concentration: The total amount of acid needs to be 40% of the final volume (80 liters).
Acid from 35% solution: 0.35x (amount of acid in liters from solution x)
Acid from 85% solution: 0.85y (amount of acid in liters from solution y) Combined acid content: 0.35x + 0.85y = 0.4 * 80 (40% of the final volume)
Solving the system of equations:
Solve the first equation for y:
y = 80 - x
Substitute y in the second equation:
0.35x + 0.85 * (80 - x) = 0.4 * 80
Simplify and solve for x:
0.35x + 68 - 0.85x = 32
-0.5x = -36
x = 72 (liters of the 35% acid solution)
Find y using the first equation:
y = 80 - 72
y = 8 (liters of the 85% acid solution)
Therefore:
You need 72 liters of the 35% acid solution.
You need 8 liters of the 85% acid solution.