A patient is prescribed a reducing total dose of Prednisolone as follows:
Day 1: 10mg
Day 2: 8mg
Day 3: 6mg
Day 4: 4mg
Day 5: 3mg
Day 6: 2mg
Day 7: 1mg
Prednisolone is supplied as 5mg and 1mg tablets. Prednisolone tablets cannot be split. Therefore, the patient needs to take a number of whole tablets. How many of each tablet strength would it be most appropriate to supply?
Answer (1)
Calculate the number of 5mg tablets needed each day by rounding up the daily dosage divided by 5.
Calculate the remaining dosage each day after accounting for the 5mg tablets.
Determine the number of 1mg tablets needed each day to meet the remaining dosage requirement (which will be 0 in this case).
Sum the total number of 5mg tablets needed over the 7 days: 10, and the total number of 1mg tablets needed: 0. The final answer is 10 of 5mg tablets and 0 of 1mg tablets .
Explanation
Understanding the Problem The patient is prescribed a reducing dose of Prednisolone over 7 days. The daily dosages are: Day 1: 10mg, Day 2: 8mg, Day 3: 6mg, Day 4: 4mg, Day 5: 3mg, Day 6: 2mg, Day 7: 1mg. Prednisolone is supplied as 5mg and 1mg tablets. The tablets cannot be split. We need to determine the most appropriate number of 5mg and 1mg tablets to supply.
Calculating 5mg Tablets First, let's calculate the number of 5mg tablets needed for each day. Since tablets cannot be split, we need to round up to the nearest whole number of tablets if the dosage is not a multiple of 5. Then, we calculate the remaining dosage that needs to be covered by 1mg tablets.
Determining Daily Tablet Needs Day 1: 10mg requires 5 10 = 2 tablets of 5mg. Remaining dosage: 10 − ( 2 × 5 ) = 0 mg. Day 2: 8mg requires 5 8 = 1.6 . Rounding up, we need 2 tablets of 5mg. Remaining dosage: 8 − ( 2 × 5 ) = − 2 mg. Since the remaining dosage is negative, we will use 0 1mg tablets. Day 3: 6mg requires 5 6 = 1.2 . Rounding up, we need 2 tablets of 5mg. Remaining dosage: 6 − ( 2 × 5 ) = − 4 mg. Since the remaining dosage is negative, we will use 0 1mg tablets. Day 4: 4mg requires 5 4 = 0.8 . Rounding up, we need 1 tablet of 5mg. Remaining dosage: 4 − ( 1 × 5 ) = − 1 mg. Since the remaining dosage is negative, we will use 0 1mg tablets. Day 5: 3mg requires 5 3 = 0.6 . Rounding up, we need 1 tablet of 5mg. Remaining dosage: 3 − ( 1 × 5 ) = − 2 mg. Since the remaining dosage is negative, we will use 0 1mg tablets. Day 6: 2mg requires 5 2 = 0.4 . Rounding up, we need 1 tablet of 5mg. Remaining dosage: 2 − ( 1 × 5 ) = − 3 mg. Since the remaining dosage is negative, we will use 0 1mg tablets. Day 7: 1mg requires 5 1 = 0.2 . Rounding up, we need 1 tablet of 5mg. Remaining dosage: 1 − ( 1 × 5 ) = − 4 mg. Since the remaining dosage is negative, we will use 0 1mg tablets.
Calculating Total Tablet Needs Now, let's calculate the total number of 5mg tablets needed: 2 + 2 + 2 + 1 + 1 + 1 + 1 = 10 tablets. Since the remaining dosages are negative, we don't need any 1mg tablets. So, the total number of 1mg tablets needed is 0.
Final Answer Therefore, the patient needs 10 tablets of 5mg and 0 tablets of 1mg.
Examples
This type of problem is common in healthcare settings where precise medication dosages are crucial. For example, when prescribing antibiotics or steroids, doctors must consider available tablet strengths and ensure the patient receives the correct dose without splitting tablets, which might compromise the medication's effectiveness or lead to inaccurate dosing. This problem demonstrates how to calculate the necessary quantities of different tablet strengths to meet a specific dosage regimen.
