Question
Chandra is a 25-year-old female who weighs 140 lbs. She has consumed three alcoholic drinks on an empty stomach within the past hour. Her blood alcohol concentration (BAC) is likely approximately _________blank.
Multiple Choice
0.05%
0.08%
0.02%
0.10%
Multiple Choice
0.05%
0.08%
0.02%
0.10%
Answers
GPT-4o mini
To estimate Chandra's Blood Alcohol Concentration (BAC) after consuming three alcoholic drinks on an empty stomach, we can use the Widmark formula, which is often used to estimate BAC.
A rough estimate for BAC for a woman can be calculated using the following formula:
\[ \text{BAC} = \frac{A}{{r \times W}} - \beta \times t \]
Where:
- \( A \) = total alcohol consumed in grams
- \( r \) = alcohol distribution ratio (approximately 0.55 for women)
- \( W \) = body weight in grams (140 lbs is approximately 63.5 kg or 63500 grams)
- \( \beta \) = alcohol elimination rate (average is about 0.017 per hour, but this factor can be omitted for the calculation if the time is short)
- \( t \) = time in hours since the consumption began (1 hour in this case)
Assuming that each standard drink contains about 14 grams of pure alcohol, three drinks will be:
\[ A = 3 \text{ drinks} \times 14 \text{ grams/drink} = 42 \text{ grams} \]
Now substituting the values into the formula:
\[ \text{BAC} = \frac{42}{{0.55 \times 63500}} \]
Calculating the denominator:
\[ 0.55 \times 63500 \approx 34925 \]
Now calculate BAC:
\[ \text{BAC} \approx \frac{42}{34925} \approx 0.0012 \]
To convert this value into a percentage, we multiply by 100:
\[ \text{BAC} \approx 0.0012 \times 100 = 0.12\% \]
However, this calculation seems to yield a higher BAC than anticipated. Let’s use another method or a quick general estimate.
Considering a general rule of thumb for BAC:
- One standard drink typically increases BAC by about 0.02% for the average person.
Thus, if Chandra consumed three drinks:
\[ \text{Estimated BAC} = 3 \times 0.02\% = 0.06\% \]
However, on an empty stomach, the effects could be more pronounced, leading us to round it up a bit.
Among the options given:
0.05%
0.08%
0.02%
0.10%
The closest and most reasonable estimate for her BAC after consuming three drinks on an empty stomach within an hour is likely **0.08%**.
A rough estimate for BAC for a woman can be calculated using the following formula:
\[ \text{BAC} = \frac{A}{{r \times W}} - \beta \times t \]
Where:
- \( A \) = total alcohol consumed in grams
- \( r \) = alcohol distribution ratio (approximately 0.55 for women)
- \( W \) = body weight in grams (140 lbs is approximately 63.5 kg or 63500 grams)
- \( \beta \) = alcohol elimination rate (average is about 0.017 per hour, but this factor can be omitted for the calculation if the time is short)
- \( t \) = time in hours since the consumption began (1 hour in this case)
Assuming that each standard drink contains about 14 grams of pure alcohol, three drinks will be:
\[ A = 3 \text{ drinks} \times 14 \text{ grams/drink} = 42 \text{ grams} \]
Now substituting the values into the formula:
\[ \text{BAC} = \frac{42}{{0.55 \times 63500}} \]
Calculating the denominator:
\[ 0.55 \times 63500 \approx 34925 \]
Now calculate BAC:
\[ \text{BAC} \approx \frac{42}{34925} \approx 0.0012 \]
To convert this value into a percentage, we multiply by 100:
\[ \text{BAC} \approx 0.0012 \times 100 = 0.12\% \]
However, this calculation seems to yield a higher BAC than anticipated. Let’s use another method or a quick general estimate.
Considering a general rule of thumb for BAC:
- One standard drink typically increases BAC by about 0.02% for the average person.
Thus, if Chandra consumed three drinks:
\[ \text{Estimated BAC} = 3 \times 0.02\% = 0.06\% \]
However, on an empty stomach, the effects could be more pronounced, leading us to round it up a bit.
Among the options given:
0.05%
0.08%
0.02%
0.10%
The closest and most reasonable estimate for her BAC after consuming three drinks on an empty stomach within an hour is likely **0.08%**.