To solve this problem, we’ll use the concept of a mixture to find the volumes of the two acid solutions needed to get a 37% acid solution.

Let:

• $V_{30}$ be the volume of the 30% acid solution.
• $V_{50}$ be the volume of the 50% acid solution.

The total volume of the mixture is 500 mL, so we have: $V_{30} + V_{50} = 500$

We also know that the mixture should be a 37% acid solution. This gives us a second equation based on the concentration: $0.30V_{30} + 0.50V_{50} = 0.37 \times 500$

Step 1: Simplify the Concentration Equation

Calculate the right side of the concentration equation: $0.37 \times 500 = 185$ So, we have: $0.30V_{30} + 0.50V_{50} = 185$

Step 2: Solve the System of Equations

We now have two equations:

1. $V_{30} + V_{50} = 500$
2. $0.30V_{30} + 0.50V_{50} = 185$

From the first equation, we can express $V_{50}$ in terms of $V_{30}$: $V_{50} = 500 - V_{30}$

Substitute $V_{50} = 500 - V_{30}$ into the second equation: $0.30V_{30} + 0.50(500 - V_{30}) = 185$

Expanding and solving for $V_{30}$: $0.30V_{30} + 250 - 0.50V_{30} = 185$ $-0.20V_{30} = -65$ $V_{30} = 325$

Now, substitute $V_{30} = 325$ back into the first equation to find $V_{50}$: $V_{50} = 500 - 325 = 175$

Solution

The volumes required are:

• $V_{30} = 325$ mL
• $V_{50} = 175$ mL

Answer

The correct answer is:

• $V_{30} = 325$ mL, $V_{50} = 175$ mL