Why It Matters: Real Numbers and Algebraic Expressions
Why Solve Linear Equations and Inequalities?
You might be surprised to learn that applications of linear equations turn up in many places besides math classrooms. Knowing how to solve them is a basic math skill used in nearly every academic discipline and in many jobs. One of the fundamental principles of solving linear equations is that of reversing or undoing mathematical operations such as addition and subtraction. To see a linear equation in action, consider one that is used by forensic scientists to calculate blood alcohol content.
Blood alcohol content (BAC) is a measurement of how much alcohol is in someone’s blood. It is usually measured in grams and as a percentage. For example, a BAC of [latex]0.30\%[/latex] is three-tenths of [latex]1\%[/latex], and it indicates that there are [latex]3[/latex] grams of alcohol for every [latex]1,000[/latex] grams of blood—which is actually a lot. A BAC of [latex]0.05\%[/latex] impairs reasoning and the ability to concentrate. A BAC of [latex]0.30%[/latex] can lead to a blackout, shortness of breath, and loss of bladder control. In most states, the legal limit for driving is a BAC of [latex]0.08%[/latex].
BAC is usually determined by the results of a breathalyzer, urinalysis, or blood test. Swedish physician E. M. P. Widmark developed an equation that works well for estimating BAC without using one of those tests. Widmark's formula is widely used by forensic scientists:
[latex]\text{B} = -0.015t +\left(\dfrac{2.84N}{Wg}\normalsize\right)[/latex]
where
- B = percentage of BAC
- t = number of hours since the first drink
- N = number of “standard drinks” (a standard drink is one [latex]12[/latex]-ounce beer, one [latex]5[/latex]-ounce glass of wine, or one [latex]1.5[/latex]-ounce shot of liquor). N should be at least [latex]1[/latex].
- W = weight in pounds
- g = gender constant: [latex]0.68[/latex] for men and [latex]0.55[/latex] for women
| Progressive Effects of Alcohol | ||
|---|---|---|
| BAC (% by vol.) | Behavior | Impairment |
| [latex]0.001–0.029[/latex] |
|
|
| [latex]0.030–0.059[/latex] |
|
|
| [latex]0.060–0.099[/latex] |
|
|
| [latex]0.100–0.199[/latex] |
|
|
| [latex]0.200–0.299 [/latex] |
|
|
| [latex]0.300–0.399[/latex] |
|
|
| [latex]0.400–0.500[/latex] |
|
|
| [latex]>0.50[/latex] |
|
|
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CC licensed content, Original
- Revision and adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Blood alcohol content. Provided by: Wikipedia Authored by: Wikipedia. Located at: https://en.wikipedia.org/wiki/Blood_alcohol_content#cite_note-0. License: CC BY-SA: Attribution-ShareAlike.
- Mai Thai Mad Man. Authored by: Nakeva Corothers. License: CC BY-NC-ND: Attribution-NonCommercial-NoDerivatives.
