How much of a solution that is 45% sulfuric acid needs to be mixed with a solution that is 90% sulfuric acid to produce 120 liters of a solution that is 60% sulfuric acid?
Just add up the acid content:
.45x + .90(120-x) = .60(120)
To find out how much of each solution is needed, we can set up an equation based on the given information.
Let's assume that x liters of the 45% sulfuric acid solution needs to be mixed with y liters of the 90% sulfuric acid solution to produce 120 liters of the 60% sulfuric acid solution.
First, we can calculate the amount of sulfuric acid in each solution.
For the 45% sulfuric acid solution:
Amount of sulfuric acid in the 45% solution = 0.45x
For the 90% sulfuric acid solution:
Amount of sulfuric acid in the 90% solution = 0.90y
The total amount of sulfuric acid in the final solution is 60% of 120 liters:
Total amount of sulfuric acid in the final solution = 0.60 * 120
Now we can set up the equation:
0.45x + 0.90y = 0.60 * 120
Simplifying the equation:
0.45x + 0.90y = 72
Since we have two unknowns (x and y), we need another equation to solve for them.
The second equation is based on the fact that the final solution is created with a total of 120 liters:
x + y = 120
Now we have a system of two equations:
0.45x + 0.90y = 72
x + y = 120
To solve this system, we can use substitution or elimination methods.
Let's use the substitution method:
Rearrange the second equation to solve for x:
x = 120 - y
Substitute this expression for x in the first equation:
0.45(120 - y) + 0.90y = 72
Simplify:
54 - 0.45y + 0.90y = 72
Combine the like terms:
0.45y = 72 - 54
0.45y = 18
Divide both sides by 0.45 to solve for y:
y = 18 / 0.45
y = 40
Now substitute the value of y back into the second equation to solve for x:
x + 40 = 120
x = 120 - 40
x = 80
Therefore, you would need 80 liters of the 45% sulfuric acid solution and 40 liters of the 90% sulfuric acid solution to produce 120 liters of a 60% sulfuric acid solution.