What quantity of 40% acid solution must be mixed with a 10% acid solution to produce 540 ml of a 20% acid solution?
I'm not sure how to set this up
add up the amount of acid present:
.40x + .10(540-x) = .20(540)
To solve this problem, we can use the concept of mixing solutions. We'll start by setting up a basic equation using the given information.
Let's denote the quantity of the 40% acid solution as x (in ml) and the quantity of the 10% acid solution as (540 - x) (since the total volume is 540 ml).
The equation can be set up as follows:
(40% acid solution)(x ml) + (10% acid solution)(540 - x ml) = (20% acid solution)(540 ml)
Now, we can solve this equation to find the value of x.
First, let's convert the percentages to decimal form:
0.40x + 0.10(540 - x) = 0.20(540)
Next, simplify the equation:
0.40x + 54 - 0.10x = 108
Combine like terms:
0.30x + 54 = 108
Subtract 54 from both sides:
0.30x = 54
Divide both sides by 0.30:
x = 180
Therefore, you would need 180 ml of the 40% acid solution and (540 - 180) = 360 ml of the 10% acid solution to produce 540 ml of a 20% acid solution.