Solution A is 25% acid and Solution B is 40% acid. How much of each is needed to make 60 liters of a solution that is 30% acid?
Not sure if this is right, but 30% acid is 5% away from Solution A, and 10% away from Solution B, so I figured the ratio needed of Solution A:Solution B was 2:1. I then did
2x+x=60
x=20
since the ratio is 2x:x, it is also 40:20.
40 liters Solution A, 20 liters Solution B.
To solve this problem, we can use a system of equations.
Let's assume that x liters of Solution A is needed and y liters of Solution B is needed.
We know that the total volume of the solution is 60 liters, so we have the equation:
x + y = 60 (Equation 1)
We also know that the resulting solution is 30% acid, so we have the equation:
(0.25x + 0.40y) / 60 = 0.30 (Equation 2)
To solve this system of equations, we can use substitution or elimination.
Let's solve using substitution. Rearrange Equation 1 to solve for x:
x = 60 - y
Substitute this value into Equation 2:
(0.25(60 - y) + 0.40y) / 60 = 0.30
Multiply through by 60 to eliminate the denominator:
0.25(60 - y) + 0.40y = 0.30 * 60
Distribute and simplify:
15 - 0.25y + 0.40y = 18
Combine like terms:
0.15y = 3
Divide by 0.15:
y = 20
Substitute this value back into Equation 1:
x + 20 = 60
Subtract 20 from both sides:
x = 40
So, you would need 40 liters of Solution A and 20 liters of Solution B to make 60 liters of a solution that is 30% acid.
To determine how much of each solution is needed to make a 30% acid solution, we can set up a system of equations based on the volume and acid concentration.
Let's assume we need x liters of Solution A (25% acid) and y liters of Solution B (40% acid) to make 60 liters of a 30% acid solution.
Equation 1: x + y = 60 (Sum of the volumes)
Equation 2: (0.25x + 0.40y) / 60 = 0.30 (Acid concentration calculation)
Now, let's solve this system of equations to find the values of x and y.
Rearrange Equation 1 to solve for x:
x = 60 - y
Substitute this expression for x in Equation 2:
(0.25 * (60 - y) + 0.40y) / 60 = 0.30
Now, we can solve for y:
(0.25 * 60 - 0.25y + 0.40y) / 60 = 0.30
(15 - 0.25y + 0.40y) / 60 = 0.30
(0.15y + 15) / 60 = 0.30
0.15y + 15 = 0.30 * 60
0.15y + 15 = 18
0.15y = 18 - 15
0.15y = 3
y = 3 / 0.15
y = 20
So, y = 20. Therefore, we need 20 liters of Solution B.
Now, we can substitute this value of y back into Equation 1 to find x:
x + 20 = 60
x = 60 - 20
x = 40
So, x = 40. This means we need 40 liters of Solution A.
To summarize, we need 40 liters of Solution A (25% acid) and 20 liters of Solution B (40% acid) to make 60 liters of a 30% acid solution.