Blood Alcohol Content Revision Notes for HSC SSCE Mathematics Standard

Blood Alcohol Content

What is blood alcohol content?

Blood Alcohol Content, or BAC, tells us how much alcohol is present in your bloodstream. It's measured as the number of grams of alcohol found in every 100 millilitres of blood.

For example, a BAC of $0.05$ means there is $0.05$ grams (or $50$ milligrams) of alcohol in every $100$ millilitres of your blood.

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Your BAC is not just about how much you drink. Multiple factors work together to determine your final BAC level, which is why two people drinking the same amount can have very different BAC values.

Your BAC is influenced by several important factors:

The number of standard drinks you consume
How much time passes while you're drinking
Your body mass (weight in kilograms)
Your gender
Your fitness level
Your overall health
How well your liver functions

BAC formulas

We can estimate blood alcohol content using mathematical formulas. There are different formulas for males and females because the body processes alcohol differently based on gender.

For males:

$BAC_{\text{Male}} = \frac{10N - 7.5H}{6.8M}$

For females:

$BAC_{\text{Female}} = \frac{10N - 7.5H}{5.5M}$

Where:

$BAC$ = Blood Alcohol Content
$N$ = Number of standard drinks consumed
$H$ = Hours spent drinking
$M$ = Mass in kilograms

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The formulas are identical except for the denominator. Males use $6.8M$ while females use $5.5M$ . This reflects biological differences in how alcohol is processed. Remember: smaller denominator for females means a higher BAC for the same inputs.

Calculating your BAC

Let's work through an example to see how we use the BAC formula in practice.

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Worked Example: Josip's BAC Calculation

Josip weighs 82 kg and has consumed 7 standard drinks over the past two hours. Police stop him for a random breath test. We need to estimate his BAC using the formula (answer correct to three decimal places).

Solution:

Step 1: Write down the formula.

$BAC_{\text{Male}} = \frac{10N - 7.5H}{6.8M}$

Step 2: Substitute the values into the formula.

We have $N = 7$ drinks, $H = 2$ hours, and $M = 82$ kg.

$BAC_{\text{Male}} = \frac{10 \times 7 - 7.5 \times 2}{6.8 \times 82}$

Step 3: Evaluate the calculation.

Step 4: Round to three decimal places.

$\approx 0.099$

Step 5: State the answer in words.

Josip's BAC is estimated to be $0.099$ .

NSW blood alcohol limits

New South Wales has three different blood alcohol limits that apply to different types of drivers. Understanding which limit applies to you is crucial for staying legal and safe.

Zero BAC (0.00)

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Zero BAC for Learners and Provisional Drivers

This applies to all learner and provisional licence holders. If you hold a learner or provisional licence, you cannot drink any alcohol before driving. Even one drink will put you over the limit and you risk losing your licence.

0.02 BAC

This limit applies to:

Drivers of heavy vehicles
Drivers carrying dangerous loads
Drivers of public vehicles (buses and taxis)

0.05 BAC

This is the standard limit for fully licensed drivers of regular vehicles.

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Police measure your BAC using either a breathalyser device or by taking and analysing a blood sample. Both methods are legally valid for determining if you're over the limit.

Using BAC tables

BAC tables provide a quick reference for estimating your blood alcohol content based on your weight and the number of drinks consumed. The table below shows estimated BAC values for consuming 1 to 6 standard drinks across five different body weights.

Drinks	Body weight (kg): 45	Body weight (kg): 55	Body weight (kg): 65	Body weight (kg): 75	Body weight (kg): 85
1	0.008	0.007	0.006	0.005	0.004
2	0.041	0.033	0.028	0.025	0.022
3	0.074	0.060	0.051	0.044	0.039
4	0.106	0.087	0.074	0.064	0.056
5	0.139	0.114	0.096	0.083	0.074
6	0.172	0.140	0.119	0.103	0.091

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Reading the Table:

Notice two important patterns:

Across rows (left to right): BAC values decrease as body weight increases. This is because a heavier person has more body mass to distribute the same amount of alcohol.
Down columns (top to bottom): BAC increases significantly with each additional drink, showing how quickly your BAC can rise.

Calculating hours to wait before driving

Once you know your BAC, you can calculate how long you should wait before it's safe to drive. Your body processes alcohol at a relatively constant rate, which allows us to estimate waiting time.

Formula:

$\text{Number of hours} = \frac{\text{BAC}}{0.015}$

The value $0.015$ represents the approximate rate at which your body eliminates alcohol from your bloodstream per hour.

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Worked Example: Terry's Waiting Time

Terry weighs 65 kg and consumes four standard drinks in one hour. Calculate how many hours Terry should wait before driving (answer to the nearest hour).

Solution:

Step 1: Write down the formula.

$\text{Number of hours} = \frac{BAC}{0.015}$

Step 2: Find Terry's BAC from the table.

Looking at the table, for someone weighing 65 kg who has consumed 4 drinks, the BAC is $0.074$ .

Substitute this value into the formula.

$\text{Number of hours} = \frac{0.074}{0.015}$

Step 3: Evaluate the calculation.

$= 4.93333...$

Step 4: Round to the nearest hour.

$\approx 5$

Step 5: State the answer in words.

Terry should wait approximately 5 hours before driving.

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Always Be Safe

The formulas and tables provide estimates only. When in doubt, wait longer or arrange alternative transport. Your safety and the safety of others should always come first.

Remember!

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Key Points to Remember:

BAC measures alcohol in blood: It's expressed as grams of alcohol per 100 millilitres of blood. A BAC of $0.05$ means $0.05$ grams of alcohol in every $100$ mL of blood.
Different formulas for males and females: Males use $BAC = \frac{10N - 7.5H}{6.8M}$ while females use $BAC = \frac{10N - 7.5H}{5.5M}$ . The only difference is the denominator ( $6.8M$ vs $5.5M$ ).
Zero BAC for learners: If you hold a learner or provisional licence, you must have zero BAC. Any alcohol consumption makes you illegal to drive.
Use tables for quick estimates: BAC tables show that heavier people generally have lower BAC for the same number of drinks, and BAC increases significantly with each additional drink.
Calculate safe waiting time: Divide your BAC by $0.015$ to estimate how many hours to wait before driving. Remember, this is an estimate—when in doubt, wait longer or arrange alternative transport.

Blood Alcohol Content (HSC SSCE Mathematics Standard): Revision Notes