1.7: Putting It Together Solving Equations and Inequalities
 Page ID
 51445
At the start of this module, you were presented with a formula commonly used by forensic scientists to calculate blood alcohol content:
\(B=0.015t +\left(\frac{2.84N}{Wg}\right)\)
where
 B = percentage of BAC
 t = number of hours since the first drink
 N = number of “standard drinks” (a standard drink is one 12ounce beer, one 5ounce glass of wine, or one 1.5ounce shot of liquor). N should be at least 1.
 W = weight in pounds
 g = gender constant: 0.68 for men and 0.55 for women
Remember Joan? When we left her, she was at a party. She had three drinks and then wanted to leave. This was worrisome. We posed the following questions:
 Where would she fall on the table of the progressive effects of alcohol after 1.5 hours?
 Would she be within the legal limit to drive after this amount of time?
The table showing the progressive effects of alcohol appears at the bottom of the page.
The information needed to answer the first question includes BAC, N, W, t and g. Of these, we know N, W, t, and g—we will need to solve for BAC.
 N = 3 standard drinks
 W = 135 pounds
 t = 1.5 hours
 g = 0.55
Using these values, we can calculate Joan’s BAC, which is the first step in answering question 1.
\(\begin{array}{l}\text{B} = 0.015t +\left(\frac{2.84N}{Wg}\right)\\\text{B} = 0.015(1.5) +\left(\frac{2.84(3)}{(135)(0.55)}\right)\\\text{B} = 0.0225 +\left(\frac{8.52}{(74.25)}\right)\\\text{B} = 0.0225 +\left(0.1147\right)\\\text{B} = 0.092\\\end{array}\)
The units of B are a percentage, so in this scenario after 1.5 hours and after consuming three standard drinks, Joan’s BAC is 0.092%.
How is Joan doing? From the table below, we can predict that she’s experiencing blunted feelings, reduced sensitivity to pain, euphoria, disinhibition, and extroversion. In addition, her reasoning, depth perception, peripheral vision, and glare recovery are probably impaired.
Question 2 asks whether she would be within the legal limit to drive. If we assume that the legal limit is 0.08%, then NO, she would not be within the legal limit to drive. One of her friends should take her car keys and help her get home.
Progressive effects of alcohol  

BAC (% by vol.)  Behavior  Impairment 
0.001–0.029 


0.030–0.059 


0.060–0.099 


0.100–0.199 


0.200–0.299 


0.300–0.399 


0.400–0.500 


>0.50 

