A chemist has one solution that is 80% acid and a second solution that is 30% acid. How many liters of each solution will the chemist need in order to make 50L of a solution that is 62% acid?
let amount of stronger solution to be used be x L
amount of weaker solution is 50-x L
.8x + .3(50-x) = .62(50)
.8x + 15 - .3x =31
.5x = 16
x = 16/.5 = 32
needs 32 L of the stronger and 36 of the weaker solution.
Ratio of 80% and 30% acids is
62-30:80-62
=32:18
=16:9
To make 50 L of 62%
Volume of 80% acid = 50*(16/25)=32 L
Volume of 30% acid = 50*(9/25)=18 L
looks like I can't do a simple subtraction
of course 50-32 = 18
as MathMate had
To solve this problem, we can use the concept of mixtures. Let's denote the volume of the 80% acid solution as x liters, and the volume of the 30% acid solution as y liters.
We know that the chemist wants to make 50L of a solution that is 62% acid. This means that the total amount of acid in the final solution will be 50L multiplied by 62%, which is 31L of acid.
We also know that the 80% acid solution contains 80% acid, which is equivalent to 0.8. So, the amount of acid in the x liters of the 80% acid solution will be 0.8x liters.
Similarly, the 30% acid solution contains 30% acid, which is equivalent to 0.3. So, the amount of acid in the y liters of the 30% acid solution will be 0.3y liters.
Since we want a total of 31L of acid in the final solution, we can write the equation:
0.8x + 0.3y = 31 (equation 1)
Also, since we want a total volume of 50L in the final solution, we can write the equation:
x + y = 50 (equation 2)
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
First, let's solve equation 2 for x:
x = 50 - y
Substituting this expression for x into equation 1, we get:
0.8(50 - y) + 0.3y = 31
Now we can solve for y. Simplifying the equation:
40 - 0.8y + 0.3y = 31
40 - 0.5y = 31
-0.5y = 31 - 40
-0.5y = -9
y = (-9) / (-0.5)
y = 18
Now that we have found the value of y to be 18, we can substitute it back into equation 2 to solve for x:
x + 18 = 50
x = 50 - 18
x = 32
Therefore, the chemist will need 32 liters of the 80% acid solution and 18 liters of the 30% acid solution in order to make 50L of a solution that is 62% acid.