Problem 60 - Calculate With Confidence

Question

Calculate the dosages to be given. Round answers to the nearest tenth as indicated (express answers in milliliters). Order: Tetracycline \(250 \mathrm{mg}\) p.o. q6h. Available: Tetracycline oral suspension labeled \(125 \mathrm{mg}\) per \(5 \mathrm{~mL}\)

Step-by-Step Solution

Answer

The dosage needed is 10 mL.

Step 1: Determine the Ordered Dose in Milligrams

The doctor has ordered 250 mg of Tetracycline to be taken every 6 hours. This means we need to administer a 250 mg dose each time.

Step 2: Analyze the Available Concentration in the Suspension

The bottle label indicates that the Tetracycline suspension has a concentration of 125 mg per 5 mL. This data will be used to find out how many milliliters contain 250 mg of the drug.

Step 3: Set Up a Proportion to Find the Required Dose in Milliliters

We know that 125 mg is found in 5 mL, and we need to find out how many mL contain 250 mg. Set up the proportion: \[\frac{125}{5} = \frac{250}{x}\]where \(x\) is the volume in mL needed to provide the 250 mg dose.

Step 4: Solve the Proportion for x

Cross-multiply and solve for \(x\):\[125x = 5 \times 250\]\[125x = 1250\]\[x = \frac{1250}{125}\]\[x = 10\]Thus, 10 mL will provide a 250 mg dose.

Step 5: Round the Result to the Nearest Tenth

The solution of the proportion provided a precise result of 10 mL, which is already rounded to the nearest tenth.

Key Concepts

Dosage Calculation

Understanding dosage calculation is key when administering medication, as it helps ensure patients receive the correct amount of the drug. In this context, dosage calculation involves determining how much of a medication is needed to achieve the desired therapeutic effect. For Tetracycline, this involves the calculation of how many milligrams (mg) are needed per dose. The doctor has ordered a 250 mg dose to be administered every 6 hours. This means the patient needs exactly 250 mg of Tetracycline each time they take the medicine.
This step is crucial because calculating the correct amount of medication helps avoid underdosing, which might not effectively treat the condition, or overdosing, which can lead to adverse effects. Ensuring precise dosage is especially critical in pediatric or geriatric patients, where a slight variation could lead to significant clinical consequences.

Proportional Reasoning

Proportional reasoning is a mathematical technique used to solve problems involving ratios. It is extremely useful in pharmaceutical calculations, especially when determining how much of a liquid medication to give based on a specific dosage requirement. In our exercise, we know that 125 mg of Tetracycline is contained in 5 mL of the suspension.
The challenge is to find out how much liquid suspension is needed to deliver a 250 mg dose as ordered by the doctor. By setting up a proportion, we form a relation where 125 mg corresponds to 5 mL, and 250 mg corresponds to an unknown amount of liquid, represented by \(x\). The proportion \[\frac{125}{5} = \frac{250}{x}\] allows us to solve for \(x\) by cross-multiplying: \[125x = 5 \times 250\]. By solving this equation, we determine the volume needed to provide the required 250 mg, ensuring that we administer the correct dosage safely.

Milliliters Conversion

Once the correct dosage in milligrams has been established and the proportional reasoning has been applied, the next step is to convert this into the volume of liquid medication needed. This involves solving the proportion we set up. From \[125x = 1250\], we find that \[x = \frac{1250}{125} = 10\].
This means that 10 milliliters (mL) of the Tetracycline suspension will deliver the needed 250 mg dose. Converting measurement units correctly is crucial, as it ensures the patient receives the exact therapeutic dosage. It's essential to be meticulous with these conversions, particularly when dealing with medications in suspension form.
After calculating, always remember to round to the nearest tenth if required. In our example, the result was already a whole number, so no rounding was necessary. However, understanding when and how to round off figures ensures clarity in communication and precision in medical practice.