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To solve this problem, we need to find the concentration of alcohol in the new 10-pint mixture.

### Given:
- 8 pints of an 8% alcohol solution
- 2 pints of a 50% alcohol solution

The new mixture will have a total volume of \(8 + 2 = 10\) pints.

### Step 1: Find the amount of alcohol in each solution.
- For the 8% solution:  
  \[ \text{Amount of alcohol} = 8\ \text{pints} \times 0.08 = 0.64\ \text{pints of alcohol} \]
- For the 50% solution:  
  \[ \text{Amount of alcohol} = 2\ \text{pints} \times 0.50 = 1\ \text{pint of alcohol} \]

### Step 2: Add the amounts of alcohol together.
Total amount of alcohol in the mixture:
\[ 0.64 + 1 = 1.64\ \text{pints of alcohol} \]

### Step 3: Calculate the concentration of alcohol in the new mixture.
The total volume of the mixture is 10 pints, so the concentration of alcohol is:
\[
\text{Concentration} = \left(\frac{1.64}{10}\right) \times 100 = 16.4\%
\]

So, the concentration of alcohol in the new 10-pint mixture is **16.4%**.

Would you like further details or have any questions?

Here are some related questions:
1. How do you calculate the concentration of a solution if the amounts of solute and solvent are different?
2. What is the general formula for finding the concentration in percentage of any mixture?
3. How does changing the ratio of two solutions affect the final concentration?
4. How can you use algebraic equations to solve similar mixture problems?
5. What are real-life applications of calculating concentrations in mixtures?

**Tip:** When mixing solutions of different concentrations, always ensure that the final concentration is calculated based on the total volume of the mixture, not just individual solutions.

Suppose 8 pints of an 8% alcohol solution is mixed with 2 pints of a 50% alcohol solution. What is the concentration of alcohol in the new 10-pint mixture?

Learn how to calculate the concentration of alcohol when mixing 8 pints of an 8% solution with 2 pints of a 50% solution. This problem covers mixture concepts, percentage calculations, and concentration formulas, suitable for Grades 6-8.

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