Find the BAC for a 125​-pound person​ who, in three​ hours, has drunk three 16​-ounce ​beers, each having a 4.0​% alcohol content.
The​ person's BAC is

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To calculate the Blood Alcohol Concentration (BAC) for the person, we can use the Widmark formula:

\[
\text{BAC} = \frac{{\text{Alcohol Consumed in grams}}}{{\text{Body Weight in grams} \times r}} - \text{Metabolism Rate} \times \text{Time}
\]

Where:
- \( r \) is the alcohol distribution ratio. For men, it's 0.68; for women, it's 0.55.
- The metabolism rate is typically around 0.015 BAC per hour.

### Step 1: Calculate the total amount of alcohol consumed
Each 16-ounce beer with a 4.0% alcohol content has:
\[
\text{Alcohol Content per Beer} = 16 \, \text{oz} \times 0.04 \times 0.789 \, \text{g/ml} \times 29.5735 \, \text{ml/oz}
\]
Where 0.789 g/ml is the density of ethanol, and 29.5735 ml is the volume in one ounce.

\[
\text{Alcohol Content per Beer} = 16 \times 0.04 \times 0.789 \times 29.5735 = 14.9 \, \text{grams of alcohol per beer}
\]
Total alcohol consumed:
\[
\text{Total Alcohol} = 14.9 \, \text{grams} \times 3 = 44.7 \, \text{grams}
\]

### Step 2: Convert body weight to grams
\[
\text{Body Weight} = 125 \, \text{pounds} \times 453.592 \, \text{grams/pound} = 56,699 \, \text{grams}
\]

### Step 3: Apply the Widmark formula
Assuming the person is male (\( r = 0.68 \)):
\[
\text{BAC} = \frac{44.7}{56,699 \times 0.68} - 0.015 \times 3
\]
\[
\text{BAC} = \frac{44.7}{38,555.32} - 0.045 = 0.00116 - 0.045 = 0.00116
\]

### Step 4: Subtract metabolism effect over 3 hours
\[
\text{BAC} = 0.00116 - 0.045 = -0.04384 \approx 0 \text{ (because BAC cannot be negative)}
\]

So, the calculated BAC after 3 hours is approximately **0.001**.

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Do you want more details or have any questions?

Here are some related questions:
1. How would the BAC change if the person weighed more?
2. How does alcohol percentage impact BAC calculations?
3. What role does gender play in BAC calculation?
4. How does drinking speed affect BAC?
5. What other factors can affect BAC?

**Tip:** Always wait an appropriate amount of time before driving after drinking alcohol to ensure your BAC is within legal limits.

Learn how to calculate Blood Alcohol Concentration (BAC) for a 125-pound person who drank three 16-ounce beers with 4.0% alcohol content over three hours. This detailed solution uses the Widmark formula and includes step-by-step calculations. Suitable for high school students studying algebra and unit conversion.

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