Question

Fred mixes a solution using two types of solutions: 0.60 liters containing 10% alcohol and 0.40 liters containing 35% alcohol.

Answer 1

The alcohol concentration of the mixed solution is 20%.

Step 1: Calculate the Amount of Alcohol in Each Solution

- For the first solution (10% alcohol): Multiply the volume of the solution by the alcohol concentration to get the amount of alcohol in liters.

- For the second solution (35% alcohol): Do the same.

Here are the calculations:

- Amount of alcohol in the first solution:

`\[ 0.60 \text{ L} * 10\% = 0.60 \text{ L} * 0.10 = 0.06 \text{ L} \]`

- Amount of alcohol in the second solution:

`\[ 0.40 \text{ L} * 35\% = 0.40 \text{ L} * 0.35 = 0.14 \text{ L} \]`

Step 2: Calculate the Total Amount of Alcohol in the Mixed Solution

- Add the amounts of alcohol from both solutions together:

`\[ 0.06 \text{ L} + 0.14 \text{ L} = 0.20 \text{ L} \]`

Step 3: Calculate the Total Volume of the Mixed Solution

- Add the volumes of the two solutions together:

`\[ 0.60 \text{ L} + 0.40 \text{ L} = 1.00 \text{ L} \]`

Step 4: Calculate the Alcohol Concentration of the Mixed Solution

- Divide the total amount of alcohol by the total volume of the solution and multiply by 100 to convert to a percentage:

`\[ \frac{0.20 \text{ L}}{1.00 \text{ L}} * 100\% = 20\% \]`

Therefore, the alcohol concentration of the mixed solution is 20%.

Answer 2

The alcohol concentration of the mixed solution is 20%.

To find the alcohol concentration of the mixed solution, you can use the weighted average formula. The formula is:

`\[ \text{Weighted Average} = \frac{\text{Sum of (Concentration} * \text{Volume)}}{\text{Total Volume}} \]`

Given that Fred has two solutions:

• Solution A: 0.60 liters containing 10% alcohol
• Solution B: 0.40 liters containing 35% alcohol

Let's calculate the weighted average:

`\[ \text{Weighted Average} = ((0.60 * 10) + (0.40 * 35))/(0.60 + 0.40) \]`

`\[ \text{Weighted Average} = (6 + 14)/(1) \]`

`\[ \text{Weighted Average} = (20)/(1) \]`

`\[ \text{Weighted Average} = 20\% \]`

Therefore, the alcohol concentration of the mixed solution is 20%.

The complete question: Fred mixes a solution using two types of solutions: 0.60 liters containing 10% alcohol and 0.40 liters containing 35% alcohol. What is the alcohol concentration of the mixed solution?