What is the estimated BAC of a man weighing approximately …

Mathematics Questions

What is the estimated BAC of a man weighing approximately 140 pounds who consumes two 12-ounce beers and one 1.5-ounce shot of liquor within one hour?

Short Answer

To calculate the Blood Alcohol Concentration (BAC), first determine total alcohol consumed from drinks (42 grams), convert body weight into grams (63560 grams for 140 lbs), and apply the gender constant (0.68 for men) to find adjusted weight (43220.8 grams). Calculate initial BAC (0.0972), convert to percentage, and adjust for metabolism over time resulting in an estimated BAC of approximately 0.08.

Step-by-Step Solution

Step 1: Calculate the Total Alcohol Consumption

Start by determining the total amount of alcohol consumed. In the U.S., a standard drink contains 14 grams of alcohol. If the individual has 2 beers and 1 shot, the total number of standard drinks is:

  • 2 beers + 1 shot = 3 standard drinks
  • 3 standard drinks x 14 g = 42 grams of alcohol

Step 2: Convert Weight and Apply Gender Constant

The next step is to convert the body weight from pounds to grams and then apply the gender constant. To do this:

  • Convert weight: 140 lbs x 454 = 63560 grams
  • Use the gender constant for men, which is 0.68.
  • Calculate adjusted grams: 63560 g x 0.68 = 43220.8

Step 3: Calculate BAC and Adjust for Time Passed

Now that you have both the total alcohol and adjusted weight, you can calculate the Blood Alcohol Concentration (BAC). Follow these steps:

  • Calculate initial BAC: 42 g of alcohol / 43220.8 = 0.000972
  • Convert to BAC percentage: 0.000972 x 100 = 0.0972
  • Adjust for time: Subtract the effect of alcohol metabolism (0.015 per hour). After 1 hour: 0.0972 – 0.015 = 0.0822.
  • The final BAC is approximately 0.08.

Related Concepts

Standard Drink

A measure of alcohol consumption in the u.s., defined as containing 14 grams of pure alcohol

Blood Alcohol Concentration (Bac)

The percentage of alcohol in a person’s bloodstream, indicating the level of intoxication

Gender Constant

A multiplier used in calculating bac based on biological sex, reflecting differences in body composition and alcohol distribution, often 0.68 for men.

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