a chemist has an 18% acid solution and a 36% acid solution. How many liters of each of these solutions should be mixed together to make 24L of 30% solution?
Enter two numbers separated by a comma
x liters of 18% acid has .18x liters of acid
y liters of 36% acid has .36y liters of acid
24 liters of 30% acid has .24*30 liters of acid
x+y = 24
.18x + .36(24-x) = .30*24
.18x + 8.64 - .36x = 7.2
.18x = 1.44
x = 8
so, 8L of 18% + 16L of 36% = 24L of 30%
8,16
To solve this problem, we can use the concept of "mixture problems" in chemistry. Let's denote the number of liters of the 18% acid solution as "x" and the number of liters of the 36% acid solution as "y."
We know that the total volume of the mixture is 24 liters, so we have the equation: x + y = 24.
We also know that the final concentration of the mixture should be 30%, which means that the amount of acid from the 18% solution plus the amount of acid from the 36% solution should equal 30% of the total volume of the mixture.
The amount of acid from the 18% solution is 18% of x, which is 0.18x.
The amount of acid from the 36% solution is 36% of y, which is 0.36y.
So, we have the equation: 0.18x + 0.36y = 0.30 * 24.
Simplifying, we get:
0.18x + 0.36y = 7.2.
Now, we can solve these two equations simultaneously to find the values of x and y.
One way to solve this system of equations is by substitution or elimination. But in this case, it's simpler to use the method of substitution.
From the first equation, we solve for x:
x = 24 - y.
We substitute this value of x into the second equation:
0.18(24 - y) + 0.36y = 7.2.
Simplifying, we get:
4.32 - 0.18y + 0.36y = 7.2.
Combining like terms:
0.18y = 7.2 - 4.32.
Simplifying further:
0.18y = 2.88.
Dividing both sides by 0.18, we find:
y = 16.
Now, we substitute this value of y back into the first equation to find x:
x + 16 = 24,
x = 24 - 16,
x = 8.
Therefore, the chemist needs to mix 8 liters of the 18% acid solution with 16 liters of the 36% acid solution to obtain 24 liters of the 30% acid solution.