A Real-World Math Assignment from Two Student Perspectives
By Dee & Dee Brown LLC
At Dee & Dee Brown LLC, we enjoy discovering how mathematics connects to everyday life. For this college assignment, we each completed a project analyzing Blood Alcohol Concentration (BAC) using linear equations, algebra, and critical thinking. Although we submitted our work individually, we both came away with a deeper appreciation for how mathematics can be used to understand public safety and make informed decisions.
What Is Blood Alcohol Concentration (BAC)?
Blood Alcohol Concentration (BAC) measures the percentage of alcohol present in a person's bloodstream. As BAC increases, a person's ability to think clearly, react quickly, maintain balance, and drive safely decreases.
In Michigan, the legal BAC limit for most drivers is 0.08%. Drivers with a BAC of 0.15% or higher are considered highly impaired and may face enhanced legal penalties due to the increased danger they pose on the road.
Understanding the Effects of Alcohol
One of the first parts of our assignment was learning how alcohol affects the body at different BAC levels.
At 0.08% BAC
At 0.08%, a person may not appear obviously intoxicated, but important driving abilities are already impaired. Reaction time slows, concentration decreases, judgment becomes less reliable, and recognizing hazards becomes more difficult. These subtle impairments make driving unsafe, even if the person does not feel drunk.
At 0.15% BAC
By 0.15% BAC, the effects become much more severe. A person may experience slurred speech, poor balance, difficulty walking, loss of coordination, and significantly impaired judgment. At this level, driving becomes extremely dangerous, which is why many states impose harsher penalties for drivers with a BAC of 0.15% or higher.
Using Algebra to Model BAC
The most interesting part of this assignment was applying algebra to model how the body naturally eliminates alcohol over time.
We analyzed the equation:
y = -0.015t + 0.12
where:
- y represents Jean's Blood Alcohol Concentration.
- t represents the number of hours after 11:00 p.m.
This equation demonstrates a linear relationship, meaning BAC decreases at a constant rate over time.
Interpreting the Equation
From the equation, we identified:
- Slope: -0.015
- Y-intercept: 0.12
The slope tells us that Jean's BAC decreases by 0.015% every hour, while the y-intercept represents her starting BAC of 0.12% at 11:00 p.m.
Tracking BAC Throughout the Night
Using the equation, we calculated Jean's BAC at different times.
| Time | Hours After 11 PM | BAC |
|---|---|---|
| 11:00 PM | 0 | 0.120% |
| 12:00 AM | 1 | 0.105% |
| 1:00 AM | 2 | 0.090% |
| 2:00 AM | 3 | 0.075% |
| 3:00 AM | 4 | 0.060% |
| 4:00 AM | 5 | 0.045% |
| 5:00 AM | 6 | 0.030% |
| 6:00 AM | 7 | 0.015% |
| 7:00 AM | 8 | 0.000% |
Seeing the values decrease at a constant rate helped reinforce the concept of linear functions and real-world modeling.
Solving Practical Problems with Algebra
We also used the equation to solve several real-life scenarios.
Jean's BAC at 12:30 A.M.
Since 12:30 a.m. is 1.5 hours after 11:00 p.m., substituting t = 1.5 into the equation gives:
BAC = 0.0975%
When Does Jean Become Legal to Drive?
To determine when Jean's BAC falls below 0.07%, we solved:
0.07 = -0.015t + 0.12
Result:
t ≈ 3.3 hours
Jean would not reach a BAC below 0.07% until approximately 3.3 hours after 11:00 p.m.
When Does BAC Reach 0.02%?
Using the same process:
0.02 = -0.015t + 0.12
Result:
t ≈ 6.7 hours
When Is All the Alcohol Gone?
Setting BAC equal to zero:
0 = -0.015t + 0.12
Result:
t = 8 hours
Jean would not completely eliminate the alcohol from her bloodstream until approximately 7:00 a.m.
Can You Sober Up Faster?
One of the biggest misconceptions about alcohol is that people can speed up the sobering process.
During our research, we learned that none of the following actually lowers Blood Alcohol Concentration:
- Drinking coffee
- Taking a cold shower
- Drinking water
- Eating food
- Exercising
While these actions may make someone feel more awake, they do not remove alcohol from the bloodstream.
The only thing that lowers BAC is time, allowing the liver to naturally metabolize the alcohol.
Donnetta's Perspective
This assignment helped me realize how mathematics can explain situations that affect everyday life. Solving the equations was valuable, but understanding the relationship between alcohol, time, and public safety made the lesson much more meaningful. It reinforced that mathematics can help people make smarter and safer decisions.
Dominique's Perspective
I enjoyed seeing how a simple linear equation could model a biological process so accurately. Instead of viewing algebra as an abstract subject, I was able to connect it to a real-world situation involving health and responsible decision-making. This assignment demonstrated that mathematics has practical applications far beyond the classroom.
Final Thoughts
Completing this assignment strengthened our understanding of linear equations while teaching an important lesson about alcohol safety. Mathematics gave us the tools to predict BAC over time, interpret data, and solve practical problems. Most importantly, we learned that there are no shortcuts to becoming sober—only time allows the body to safely process alcohol.
Assignments like this remind us that education is most powerful when it connects academic concepts with real-life experiences.
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