What is the estimated BAC of…

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 in one hour?

Short Answer

To calculate Blood Alcohol Concentration (BAC), first identify the total alcohol consumed, which is 1.8 oz (51 grams). Using the formula BAC = (Grams of Alcohol) / (Weight in grams x Gender Constant), and applying it to a 140-pound male, the calculated BAC is 0.11%.

Step-by-Step Solution

Step 1: Understand Alcohol Consumption

To calculate the Blood Alcohol Concentration (BAC), it is crucial to account for the amount and type of alcohol consumed. In this case, the individual consumed:

  • Two 12-ounce beers, which contain 0.6 oz of alcohol each.
  • One 1.5 oz shot of 40% liquor, which also has 0.6 oz of alcohol.
  • In total, he consumed 1.8 oz of alcohol.

Step 2: Convert Alcohol Quantity to Grams

Once you have the total amount of alcohol consumed in ounces, convert this figure to grams. The conversion is straightforward:

  • 1.8 oz of alcohol is equivalent to 51 grams of alcohol.
  • This is a key figure needed for calculating the BAC.

Step 3: Calculate the BAC

To find the BAC, use the following formula: BAC = (Grams of Alcohol) / (Weight in grams x Gender Constant). For the individual weighing 140 pounds (63560 grams) and using the male constant of 0.68:

  • Set up the equation: 51 / (63560 x 0.68).
  • Calculate the result, which gives 0.0011.
  • Finally, multiply by 100 to convert to BAC percentage: 0.11.

Related Concepts

Alcohol consumption

The total amount and type of alcoholic beverages consumed, which affects the calculation of blood alcohol concentration (bac).

Grams of alcohol

The mass of alcohol converted from ounces to grams, essential for determining the bac accurately.

Bac calculation

A mathematical formula that estimates blood alcohol concentration using the grams of alcohol consumed, the individual’s weight, and a gender constant.

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