Maths in Healthcare Context: Dosage Calculations, Conversions, and BMI

This assignment focuses on applying mathematical principles within a healthcare setting. It provides detailed solutions to various dosage calculation problems, including liquid and tablet medications, considering stock strengths and required doses. The assignment covers different scenarios, such as calculating the volume of medication to be administered, determining the number of tablets needed, and addressing situations involving suspensions. Furthermore, it includes conversion exercises involving units of measurement (e.g., inches to meters, Fahrenheit to Celsius, weight conversions) and the application of Body Mass Index (BMI) calculations to assess patient weight status. The assignment also incorporates the analysis of patient data, such as peak flow rates, to interpret trends and understand patient health conditions, with a focus on practical application of mathematical concepts in clinical practice.

Maths in a Healthcare Context

Table of Contents
INTRODUCTION...........................................................................................................................1
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Ques 1.
State the formula you would use to calculate the volume of a required dose.
Solution:
For liquid dosage –
Volume of dose to be given = Required dose x Stock Volume
Stock Dose
Ques 2.
A patient is prescribed 60mg of Pethidine. The stock solution strength is 10g in 200ml What
volume would be needed to give the required dose. State the formula used.
Solution: Volume of dose to be given = Required dose x Stock Volume
Stock Dose
= 60mg x 200ml
10g
= 60mg x 200ml
10000g
= 1.2ml
Ques 3.
An injection of morphine 10 mg is prescribed. A stock ampoule contains morphine 20 mg in 1
ml. The volume to be drawn up for injection will be equal to 1 ml/ less than 1 ml/ more
than 1 ml
Solution: Volume of dose to be given = Required dose x Stock Volume
Stock Dose
= 10mg x 1ml
20mg
= 0.5ml
So, volume of morphine in injection to be drawn up will be less than 1ml.
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Ques 4.
A patient is to receive an injection of ondansetron 6 mg. Stock ampoules contain ondansetron
4mg/2 ml. The volume to be drawn up for injection is equal to 2 ml/ less than 2 ml/ more
than 2 ml.
Solution: Volume of dose to be given = Required dose x Stock Volume
Stock Dose
= 4mg x 2ml
6mg
= 1.3ml
So, volume of ondansetron in injection to be drawn up will be less than 2ml
Ques 5.
Furosemide (frusemide) 80 mg is ordered. Ampoules contain furosemide (frusemide) 250 mg in
5 ml. The volume required for injection is equal to 5 ml/ less than 5 ml/ more than 5 ml
Solution: Volume of dose to be given = Required dose x Stock Volume
Stock Dose
= 80mg x 5ml
250mg
= 1.6ml
So, volume of furosemide in injection to be drawn up will be less than 5ml
Ques 6.
50 mg of captopril is prescribed for heart failure. On hand are tablets of strength 25mg. How
many tablets should be given?
Solution: Volume of dose to be given = Required dose
Stock Dose
= 50mg
25mg
= 2
So, 2 tablets of captopril are needed to be given.
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Ques 7.
A patient needs 15mg of codeine The stock tablets are 30mg. How many tablets should be
given?
Solution: Volume of dose to be given = Required dose
Stock Dose
= 15mg
30mg
= ½
So, ½ tablet of codeine is needed to be given.
Ques 8.
Many oral medications in liquid form are suspensions. What must be done to those medications
before measuring out the required volume?
Solution: As suspension contain small amount of solid drug, therefore, before measuring out the
required volume, it needs to shake the bottle properly, to completely dissolve it. This would help
in getting right amount of medicine every time.
Ques 9.
A suspension contains penicillin 250 mg/5ml. How many milligrams of penicillin are in
Given,
Suspension contains penicillin = 250mg per 5ml
so, in 1ml = 250 / 5 = 50mg
a) 10ml
Amount of penicillin in 10ml = 50 x 10 = 500mg
b) 25ml
Amount of penicillin in 25ml = 50 x 25 = 1,250mg = 1g 250mg
c) 45ml
Amount of penicillin in 45ml = 50 x 45 = 2,250mg = 2g 250mg
3

Ques 10.
A patient is prescribed 500 mg of erythromycin, orally. Calculate the volume required if the
suspension on hand has strength of 250 mg/5 ml.
Solution: Volume of dose to be given = Required dose x Stock Volume
Stock Dose
= 250mg x 5ml
500mg
= 2.5ml
Ques 11.
When prescribing tablets for patients, the stock strength does not always match the dose
prescribed. State the formula you would use to calculate the number of tablets needed.
Answer: Number of tablets = Required dose / stock dose
Ques 12.
How many tablets containing 50mcg will be required to give a dose of 0.1mg? State the formula
used
Solution: Number of tablets = Required dose / stock dose
= 50mcg
0.1mg
= 50mcg
100mcg
= ½ tablet
Ques 13.
A drug in tablet form is prescribed. The required dosage is 90 mg. The tablets are in 30mg each.
How many tablets should be dispensed?
Solution: Number of tablets = Required dose / stock dose
= 90g
30mg
= 3 tablets
4

Ques 14.
50 mg of a drug is prescribed. The drug is in liquid form and is to be given orally. It has strength
of 25mg per 5 ml spoon. How many spoonfuls are required? What volume is dispensed?
Solution: Volume dispensed = Required dose x Stock Volume
Stock Dose
= 25mg x 5ml
50mg
= 2.5ml
Number of spoonfuls = 2.5 / 5 = 2 spoonfuls
Ques 15.
A patient requires 20 mg of a drug in liquid form. If the stock contains 10 mg in 2 ml, what
volume of the drug should be drawn up?
Solution: Volume dispensed = Required dose x Stock Volume
Stock Dose
= 10mg x 2ml
20mg
= 1ml
Ques 16.
50 mg of a drug is prescribed. The drug is in liquid form and is to be given orally. It has strength
of 10 mg per 5 ml spoon. How many spoonfuls are required? What volume is dispensed?
Solution: Volume dispensed = Required dose x Stock Volume
Stock Dose
= 10mg x 5ml
50mg
= 1ml
Number of spoonfuls = 1 / 5 = 0.2spoonful
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Ques 17.
A patient is ordered paracetamol 1g, orally. Stock on hand is 500mg tablets. Calculate the
number of tablets required.
Solution: Number of tablets = Required dose / stock dose
= 1g
500mg
= 1000mg
500mg
= 2 tablets
Ques 18.
How many 30 mg tablets of codeine are needed for a dose of 0.06gram?
Solution: Number of tablets = Required dose / stock dose
= 0.06g
30mg
= 60mg
30mg
= 2 tablets
Ques 19.
750 mg of ciprofloxacin is required. On hand are tablets of strength 500 mg. How many tablets
should be given?
Solution: Number of tablets = Required dose / stock dose
= 750mg
500mg
= 1 ½ tablets
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Ques 20.
You are asked to calculate the dose of medication for a patient based on the patient weight. What
is the appropriate formula to calculate the dosage for weight?
Answer: Required Dosage = Weight in kg * Dosage per kg
Ques 22.
Conversion
5 Ft = 12 x 5 = 60 inches
5 yards = 5 x 3 = 15 feet
3 miles = 3 x 1760 = 5280yards
6 pounds = 6 x 16 = 96 ounces
5 stones = 5 x 14 = 70 pounds
2 tons = 2 x 2240 = 4480 pounds
4 gallons = 4 x 8 = 32 pints
7 feet = 7 x 12 = 98 inches
2 yards = 2 x 36 = 72 inches
11 yards = 11 x 3 = 33 feet
5 pounds = 5 x 16 = 80 ounces
72 inches = 72 / 12 = 6 feet
Conversion of weight in kg to pounds
6kg = 6 x 2.2 = 13.2 pounds
8kg = 8 x 2.2 = 17.2 pounds
15kg = 15 x 2.2 = 33.0 pounds
32kg = 32 x 2.2 = 70.4 pounds
45kg = 45 x 2.2 = 99.0 pounds
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Conversion of weight in pounds to kg
10pounds = 10 / 2.2 = 4.5kg
18pounds = 18 / 2.2 = 8.2kg
25pounds = 25 / 2.2 = 11.4kg
40pounds = 40 / 2.2 = 18.2 pounds
56pounds = 56 / 2.2 = 25.5 pounds
Ques 23.
Convert the following from Fahrenheit to centigrade
Formula for F to C =
C = (F – 32) * 5/9
92F = (92 – 32) * 5/9 = 33.33 C⁰
86F = (86 – 32) * 5/9 = 30 C⁰
73F = (73 – 32) * 5/9 = 22.78 C⁰
56F = (56 – 32) * 5/9 = 13.33 C⁰
49F = (49 – 32) * 5/9 = 9.44 C⁰
90F = (90 – 32) * 5/9 = 32.23 C⁰
43F = (43 – 32) * 5/9 = 6.11 C⁰
99F = (99 – 32) * 5/9 = 37.22 C⁰
79F = (79 – 32) * 5/9 = 26.11 C⁰
Ques 24.
Convert the following from Centigrade to Fahrenheit
Formula for C to F =
F = (C * 9/5) + 32 1.8
22 C = (22 * 9/5) + 32 = 71.6 F⁰
37 C = (37 * 9/5) + 32 = 98.6 F⁰
29 C = (29 * 9/5) + 32 = 84.2 F⁰
17 C = (17 * 9/5) + 32 = 57.5 F⁰
33 C = (33 * 9/5) + 32 = 91.4F⁰
42 C = (42 * 9/5) + 32 = 107.6 F⁰
31 C = (31 * 9/5) + 32 = 61.2 F⁰
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11 C = (11 * 9/5) + 32 = 51.8 F⁰
2 C = (2 * 9/5) + 32 = 35.6 F⁰
Ques 25.
Change each of these distances in inches to meters
48 inches = 48 / 39.37 = 1.2m
52 inches = 52 / 39.37 = 1.3m
60 inches = 60 / 39.37 = 1.5m
75 inches = 75 / 39.37 = 1.9m
100 inches = 100 / 39.37 = 2.5m
Ques 26.
If a gentleman is 6 feet tall and 140lb. According to the given chart, is this gentleman
underweight, normal, overweight or obese?
Formula to calculate BMI
= weight / height
so, BMI of gentleman = 140/6 = 265.8
As per Graph, the Gentleman has normal BMI
Ques 27
A woman is 5’7” and weighs 49.9kgs. According to this chart is she underweight, normal,
overweight or obese? Show your working on the chart
As per graph, the women is underweight
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Ques 28.
Approximately what is the normal weight range for a woman who is 4ft 11inches tall?
Answer: 42 to 54.4kg
Approximately what is the underweight range for a woman who is 5ft 5inches tall?
Answer: 36.3 to 50kg
A woman who is 5ft 8 inches tall weighs 11 stone – is she underweight, of normal weight or
overweight?
Answer: Normal weight
If a woman of 5ft 6 inches tall weighs 7 stone, by approximately how much is she underweight?
Answer: Underweight
Approximately what is the normal weight range for a man who is 4ft 11inches tall?
Answer: Approx. 42kg
Approximately what is the underweight range for a man who is 5ft 5inches tall?
Answer: 36.3 to 50kg
A man who is 5ft 8 inches tall weighs 11 stone – is he underweight, of normal weight or
overweight?
Answer: Underweight
If a man of 5ft 6 inches tall weighs 7 stone, by approximately how much is he underweight?
Answer: Underweight
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