Open MathNSWGitHub ↗

BAC and medication formulas

Substitute into the blood alcohol content (BAC) formula for males and females; apply Fried's rule and Young's rule to calculate appropriate medication doses for children; determine whether a BAC is below the legal driving limit and find how long to wait before driving.

Worked examples

Calculating BAC using the male formula

Straightforward

Problem

A male weighing 80 kg has consumed 4 standard drinks over 2 hours. Use BACmale=10N−7.5H6.8M\text{BAC}_\text{male} = \dfrac{10N - 7.5H}{6.8M} to find his blood alcohol content correct to 3 decimal places.

Finding a child's dose using Young's rule

Moderate

Problem

A 10-year-old child requires medication. The adult dose is 440 mg. Use Young's rule (dose=age (years)×adult doseage (years)+12)\left(\text{dose} = \dfrac{\text{age (years)} \times \text{adult dose}}{\text{age (years)} + 12}\right) to find the child's recommended dose.

Finding the minimum wait time before driving

Challenging

Problem

A female weighing 55 kg consumes 7 standard drinks at 8:00 pm and drinks nothing after that. Her BAC at HH hours after 8:00 pm is given by BACfemale=10N−7.5H5.5M\text{BAC}_\text{female} = \dfrac{10N - 7.5H}{5.5M}. Find the minimum number of complete hours she must wait before her BAC falls below 0.05.

Practise

Q1·Straightforward
A male weighing 75 kg has consumed 3 standard drinks over 1 hour. Use the formula BACmale=10N−7.5H6.8M\text{BAC}_\text{male} = \dfrac{10N - 7.5H}{6.8M} to find his blood alcohol content correct to 3 decimal places, where NN is the number of standard drinks consumed, HH is the number of hours elapsed and MM is body mass in kg.
Q2·Straightforward
A female weighing 60 kg has consumed 2 standard drinks over 1 hour. Use the formula BACfemale=10N−7.5H5.5M\text{BAC}_\text{female} = \dfrac{10N - 7.5H}{5.5M} to find her blood alcohol content correct to 3 decimal places.
Q3·Straightforward
A male weighing 90 kg has consumed 5 standard drinks over 2 hours. Use BACmale=10N−7.5H6.8M\text{BAC}_\text{male} = \dfrac{10N - 7.5H}{6.8M} to find his blood alcohol content correct to 3 decimal places.
Q4·Straightforward
Fried's rule gives the recommended dose for a child as dose=age (months)×adult dose150\text{dose} = \dfrac{\text{age (months)} \times \text{adult dose}}{150}. Find the recommended dose in mg for an 18-month-old child when the adult dose is 200 mg.
Q5·Moderate
Young's rule gives the recommended dose for a child as dose=age (years)×adult doseage (years)+12\text{dose} = \dfrac{\text{age (years)} \times \text{adult dose}}{\text{age (years)} + 12}. Find the recommended dose in mg for an 8-year-old child when the adult dose is 500 mg.
Q6·Moderate
Using Fried's rule (dose=age (months)×adult dose150)\left(\text{dose} = \dfrac{\text{age (months)} \times \text{adult dose}}{150}\right), find the recommended dose in mg for a 30-month-old child when the adult dose is 250 mg.
Q7·Moderate
Using Young's rule, find the recommended dose in mg for a 6-year-old child when the adult dose is 360 mg.
Q8·Moderate
A female weighing 55 kg has consumed 4 standard drinks over 2 hours. Using BACfemale=10N−7.5H5.5M\text{BAC}_\text{female} = \dfrac{10N - 7.5H}{5.5M}, find her blood alcohol content correct to 3 decimal places.
Q9·Challenging
A male weighing 80 kg has consumed 5 standard drinks over 2 hours. Using BACmale=10N−7.5H6.8M\text{BAC}_\text{male} = \dfrac{10N - 7.5H}{6.8M}, calculate his blood alcohol content correct to 3 decimal places, then determine whether he is legally able to drive if the limit is BAC <0.05< 0.05. Give the BAC as your numerical answer.
Q10·Challenging
A female weighing 60 kg consumes 6 standard drinks at 9:00 pm and drinks nothing after that. Her BAC at HH hours after 9:00 pm is given by BACfemale=10N−7.5H5.5M\text{BAC}_\text{female} = \dfrac{10N - 7.5H}{5.5M}. Find the minimum number of complete hours she must wait before her BAC falls below 0.05.
Q11·Challenging
A male weighing 70 kg has consumed 3 standard drinks and waited exactly 1 hour before considering driving. Using BACmale=10N−7.5H6.8M\text{BAC}_\text{male} = \dfrac{10N - 7.5H}{6.8M}, calculate his BAC correct to 3 decimal places and determine whether he is below the 0.05 legal limit. Give the BAC as your numerical answer.
Q12·Challenging
A male weighing 90 kg consumes 8 standard drinks at 7:00 pm and drinks nothing after that. His BAC at HH hours after 7:00 pm is given by BACmale=10N−7.5H6.8M\text{BAC}_\text{male} = \dfrac{10N - 7.5H}{6.8M}. Find the minimum number of complete hours after 7:00 pm before his BAC first falls below 0.05.