You drink a 12 oz beer that has 4.5% ABV.

You drink a 12 oz beer that has 4.5% ABV. The rest of the calories, other than alcohol, come from carbohydrates. If the beer contains 140 calories, how many calories from carbohydrates did you ingest?

The Correct Answer and Explanation is:

To solve this, we need to determine how many calories come from alcohol and then subtract that from the total calories to find how many calories come from carbohydrates.

Step-by-step:

1. Calculate the calories from alcohol:
   • The beer is 12 oz and has 4.5% ABV (alcohol by volume).
   • Alcohol provides about 7 calories per gram.
   • The density of ethanol (alcohol) is about 0.789 g/ml.
   First, calculate the amount of alcohol in the beer: Volume of alcohol=12 oz×4.5%=0.54 oz of alcohol\text{Volume of alcohol} = 12 \, \text{oz} \times 4.5\% = 0.54 \, \text{oz of alcohol}Volume of alcohol=12oz×4.5%=0.54oz of alcohol Convert ounces to milliliters (1 oz = 29.5735 ml): 0.54 oz×29.5735 ml/oz=15.95 ml of alcohol0.54 \, \text{oz} \times 29.5735 \, \text{ml/oz} = 15.95 \, \text{ml of alcohol}0.54oz×29.5735ml/oz=15.95ml of alcohol Now, convert the volume of alcohol to grams (since density = mass/volume): Mass of alcohol=15.95 ml×0.789 g/ml=12.59 g of alcohol\text{Mass of alcohol} = 15.95 \, \text{ml} \times 0.789 \, \text{g/ml} = 12.59 \, \text{g of alcohol}Mass of alcohol=15.95ml×0.789g/ml=12.59g of alcohol Finally, calculate the calories from alcohol: Calories from alcohol=12.59 g×7 cal/g=88.13 calories from alcohol\text{Calories from alcohol} = 12.59 \, \text{g} \times 7 \, \text{cal/g} = 88.13 \, \text{calories from alcohol}Calories from alcohol=12.59g×7cal/g=88.13calories from alcohol
2. Calculate the calories from carbohydrates:
   • The total calories in the beer are 140.
   • Subtract the calories from alcohol to find the calories from carbohydrates:
   Calories from carbohydrates=140−88.13=51.87 calories from carbohydrates\text{Calories from carbohydrates} = 140 – 88.13 = 51.87 \, \text{calories from carbohydrates}Calories from carbohydrates=140−88.13=51.87calories from carbohydrates

Conclusion:

The number of calories from carbohydrates in the beer is approximately 51.87 calories.

This explanation involved breaking down the volume of alcohol into grams and calculating its contribution to the total calorie count. The rest of the calories come from carbohydrates, which in this case was around 52 calories.