Certainly! Let's go through each part of the question step-by-step.
### Part A:
In New Mexico, it is illegal to drive with a blood alcohol concentration (BAC) of 0.08 or more if you are 21 or over.
### Part B:
To calculate the BAC, we will use the given formula:
[tex]\[
BAC = \frac{600n}{w(0.6n + 169)}
\][/tex]
where [tex]\( w \)[/tex] is the body weight in pounds, and [tex]\( n \)[/tex] is the number of drinks per hour.
Let's assume the body weight is 150 pounds (you can replace this with your own body weight if different). We are given that [tex]\( n = 4 \)[/tex] (i.e., 4 drinks per hour).
Now, we substitute [tex]\( w = 150 \)[/tex] and [tex]\( n = 4 \)[/tex] into the formula:
[tex]\[
BAC = \frac{600 \times 4}{150 \times (0.6 \times 4 + 169)}
\][/tex]
Calculate the denominator:
[tex]\[
150 \times (0.6 \times 4 + 169) = 150 \times (2.4 + 169) = 150 \times 171.4 = 25710
\][/tex]
Then calculate the numerator:
[tex]\[
600 \times 4 = 2400
\][/tex]
Now divide the numerator by the denominator:
[tex]\[
BAC = \frac{2400}{25710} \approx 0.0933
\][/tex]
So, the BAC for a person weighing 150 pounds who has 4 drinks per hour is approximately 0.0933.
### Part C:
From the calculation in Part B, you can draw the following conclusion:
The calculated BAC for a person weighing 150 pounds who consumes 4 drinks in an hour is approximately 0.0933. Since the legal limit for BAC in New Mexico (and most other U.S. states) is 0.08, this person's BAC is above the legal limit. Therefore, it would be illegal for this person to drive under these conditions.
In general, it is important to be aware of the effects of alcohol on your body and how it influences your ability to drive safely. Always ensure your BAC is within the legal limits or refrain from driving if you have consumed alcohol.
