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Algebra - Blood Alcohol Content (BAC).
Test Yourself 1.


 

For the following questions, you will need one of the following formulae:

where N is the number of standard drinks

 

Finding BAC only. 1.
Number of standard drinks
White wine Red wine
Small glass Large glass Small glass Large glass
0.9 1.4 1.0 1.5

A woman weighing 62 kg drinks three small glasses of white wine and two large glasses of red wine between 8 pm and 1 am.

What would her bloood alcohol content (BAC) be at 1 am? (answer correct to 3 decimal places).

Answer.BAC = 0.057.
  2. Charlotte weighs 55 kg and she consumed 4 standard drinks in the past three hours. She then left but was stopped by the police for a random breath test shorthly after.

What was Charlotte's blood alcohol content (BAC)?

Answer.BAC = 0.051.
 

3. At a party, Beccy begins drinking at 6:45 pm and she has 7 standard drinks before she stops drinking at 11:15 pm. If Charlotte has a weight of 58 kg, calculate her BAC (to 3 decimal places).

Answer.BAC = 0.114.
  4.
  5.
Finding number of standard drinks only. 6. How many grams of alcohol are there in one standard drink?
Answer.10 grams in 1 standard drink.
  7. Georgia weighs 62 kg. She has been drinking for three hours and registers a blood alcohol reading of 0.08.

How many standard drinks had Georgia consumed?
Answer.5 standard drinks (4.978).
  8.
  9.
  10.
Finding hours of drinking only. 11. Ben weighs 70 kg and has bought a six-pack of an alcoholic beverage to drink at a party. Each drink in the pack is the equivalent of one standard drink.

What is the minimum length of time over which Ben must consume all six drinks if he is to stay below the 0.05 level of BAC at the end of the party?
(answer to the nearest quarter of an hour).
  12.
  13.
  14.
  15.
Finding time before BAC is below the threshold. 16. Chloe holds a provisional licence. Her allowable Blood Alcohol Content (BAC) to drive is zero.

If she consumed 10 standard drinks from 10 pm to 2 am, what is the earliest time that our 62 kg Chloe could legally drive home?

Earliest time is 11:20 am.
  17. Rosey, who has a mass of 60 kg, arrives at an end of year party at 8 pm and immediately begins to celebrate by opening a can of alcoholic drink she has brought with her. By 11 pm, Rosey has consumed the four pack of drinks. Each can contains the equivalent of 1.5 standard drinks.

Using the formula , estimate (to the nearest quarter of an hour), how long it will take for Rosey's BAC to reach zero.

Answer.Rosey's BAC would be 0.1136
so 7 hours 30 min.
  18. My friend Ben went to a party last Saturday night. He is no longer on a Provisional licence.

Ben had a few drinks but when he stopped drinking at 11:00 pm, he (conscientously) measured his BAC because he wanted to drive some of his friends home.
His BAC was 0.07625.

Using the standard formula ,


(i) at what time did Ben reach the 0.05 limit and so could start driving his friends home?

(ii) At that time, did Ben have any friends?

Answer.(i) Length of time is 1 hours 45 mins - so it would be 12:45 am.
(ii) Yes - they waited for him (being friends).
  19.
  20.
Combination questions. 21. Louisa has a mass of 54 kg and she has been drinking alcohol for the last 3 hours.

Her present BAC is estimated to be 0.06.

(i) Show that Louisa has consumed 4 standard drinks during this period of time.

(ii) One standard drink contains 10 grams of alcohol. Louisa's body can break down alcohol at the rate of 8.6 grams/hour.

If Louisa stops drinking alcohol now, after how many more hours and minutes should Louisa BAC be close to zero?

Answer.(i) 4 drinks
(ii) 4 hours).
  22. Shane, who is a 28 year old male, weighs 80 kg. He consumes five cans of an alcoholic beverage in two hours. Each can contains the equivalent of 1.5 standard drinks.

(i) What is Shane's blood alcohol content (BAC) at the end of 2 hours (answer to 2 significant figures)?

(ii) The formula can be used to estimate approximately how long it will take for a person's blood alcohol content (BAC) to reach zero. How long will it take Shane to reach zero.

 
  23. Tara has been consuming alcoholic drinks at a party for the last three hours. She has a mass of 54 kg. Her BAC is measured to be 0.06.

(i) Determine the number of standard drinks Tara has consumed during this period.

(ii) Using the formula , estimate the time (to the nearest 20 minutes) for Tara's BAC to return to zero.

Answer.(i) 4 standard drinks.
(ii) 4 hours 40 min.
  24. Amy has 3 ‘large’ glasses of wine over two and a half hours. A ‘large’ glass of wine is 1·5 standard drinks.

Amy weighs 53 kg.

The formula to calculate her Blood Alcohol Content is shown above.

(i) Calculate Amy’s Blood Alcohol Content after two and a half hours.

(ii) If Amy has no more alcohol, determine how long she must wait until her Blood Alcohol Content returns to zero.

Answer.(i) BAC = 0.090.
(ii) 6 hours.
  25.