A chemist has a bottle of a 10% acid solution
and a bottle of a 30% acid solution. He mixes the
solutions together to get 500 mL of a 25% acid
solution. How much of the 30% solution did
he use?
.3 x + [.1 (500 - x)] = .25 * 500
To determine how much of the 30% acid solution the chemist used, we can set up a system of equations. Let's call the volume of the 10% acid solution "x" and the volume of the 30% acid solution "y".
We have two equations based on the given information:
Equation 1: The total volume of the mixture is 500 mL.
x + y = 500
Equation 2: The resulting solution is 25% acid solution, which means that 25% of the 500 mL is acid.
(0.10x + 0.30y) = 0.25(500)
Now, we can solve this system of equations to find the values of x and y.
First, let's rearrange Equation 2 to isolate one variable:
0.10x + 0.30y = 0.25(500)
0.10x + 0.30y = 125
Next, let's multiply both sides of Equation 1 by 0.10 to prepare for elimination:
0.10(x + y) = 0.10(500)
0.10x + 0.10y = 50
Now, let's subtract the modified Equation 1 from Equation 2 to eliminate x:
0.10x + 0.30y - 0.10x - 0.10y = 125 - 50
0.20y = 75
Divide both sides of the equation by 0.20:
y = 75 / 0.20
y = 375 mL
Therefore, the chemist used 375 mL of the 30% acid solution.
Let x represent the amount of the 30% acid solution used by the chemist.
Step 1: Write down the equation for the total amount of acid in the mixture.
0.1(500 - x) + 0.3x = 0.25(500)
Step 2: Simplify the equation.
50 - 0.1x + 0.3x = 125
Step 3: Combine like terms.
0.2x = 75
Step 4: Divide both sides by 0.2 to solve for x.
x = 375
Therefore, the chemist used 375 mL of the 30% acid solution.