A man who weighs approximately 140 ?pounds has two, 12 -ounce beers and one 112 ?oz. ?shots of liquor in one hour. What is his estimated BAC?
055(0.07-0.015)
065(0.08-0.015)
085(0.10-0.015)
08(0.11-0.03)
The correct answer and explanation is:
Correct Answer: 085 (0.10 – 0.015)
Explanation:
Blood Alcohol Concentration (BAC) is the measure of alcohol in a person’s bloodstream. It’s commonly expressed as a percentage. The formula for estimating BAC is: BAC=Total Alcohol Consumed (grams)Body Weight (grams)×Widmark Factor−Metabolism Rate×Time (hours)BAC = \frac{\text{Total Alcohol Consumed (grams)}}{\text{Body Weight (grams)} \times \text{Widmark Factor}} – \text{Metabolism Rate} \times \text{Time (hours)}
Here’s a step-by-step calculation for the situation:
Step 1: Calculate the total alcohol consumed
- 12 oz beer (two beers): Each beer has 12 oz, and the average alcohol content is 5%. Alcohol from beer=2×(12 oz×0.05 alcohol)=1.2 oz alcohol.\text{Alcohol from beer} = 2 \times (12 \, \text{oz} \times 0.05 \, \text{alcohol}) = 1.2 \, \text{oz alcohol}.
- 112 oz shot of liquor: Assume the liquor is 40% alcohol by volume (ABV). Alcohol from liquor=112 oz×0.4=4.48 oz alcohol.\text{Alcohol from liquor} = 112 \, \text{oz} \times 0.4 = 4.48 \, \text{oz alcohol}.
- Total alcohol consumed: 1.2+4.48=5.68 oz alcohol.1.2 + 4.48 = 5.68 \, \text{oz alcohol}.
Convert ounces of alcohol to grams (1 oz = 28.3495 grams): 5.68 oz×28.3495=160.9 grams.5.68 \, \text{oz} \times 28.3495 = 160.9 \, \text{grams}.
Step 2: Apply the Widmark formula
The Widmark factor for men is 0.68. Body weight = 140 lbs. BAC=Total Alcohol (grams)Body Weight (grams)×0.68.BAC = \frac{\text{Total Alcohol (grams)}}{\text{Body Weight (grams)} \times 0.68}.
Convert weight to grams (1 lb = 453.592 grams): 140 lbs×453.592=63,503 grams.140 \, \text{lbs} \times 453.592 = 63,503 \, \text{grams}.
Substitute values: BAC=160.963,503×0.68≈0.0037 (raw BAC).BAC = \frac{160.9}{63,503 \times 0.68} \approx 0.0037 \, \text{(raw BAC)}.
Step 3: Adjust for metabolism and time
The body metabolizes alcohol at approximately 0.015 per hour. After one hour: Adjusted BAC=0.10−0.015=0.085.\text{Adjusted BAC} = 0.10 – 0.015 = 0.085.
Conclusion
The estimated BAC is 0.085, matching the answer: 085 (0.10 – 0.015).