Question

Calculate the following medication dosages using the dimensional analysis method. Use medication labels or information provided. Label answers correctly: tab, caps, mL. Answers expressed in milliliters should be expressed to the nearest tenth, except where indicated. Order: Solu-Medrol \(175 \mathrm{mg}\) IV daily. Available: Solu-Medrol labeled \(500 \mathrm{mg}\) per \(8 \mathrm{~mL}\) ______

Short answer

2.8 mL

Step-by-step solution

Understand the Order

The doctor's order is to administer 175 mg of Solu-Medrol intravenously once a day. This is what we'll need to calculate how many milliliters are required.

Analyze the Availability

The available concentration of Solu-Medrol is labeled as 500 mg per 8 mL. This means that for every 500 mg of the medication, 8 mL of the solution is required.

Set Up the Ratio

Set up the proportional ratio using the available information to find out how many milliliters correspond to 175 mg:\[\frac{500 \, \text{mg}}{8 \, \text{mL}} = \frac{175 \, \text{mg}}{x \, \text{mL}}\]where \(x\) is the amount of solution we need in mL.

Cross Multiply and Solve for x

Cross multiply to solve for \(x\):\[500 \times x = 175 \times 8\]\[500x = 1400\]Now divide both sides by 500 to solve for \(x\):\[x = \frac{1400}{500} = 2.8\] mL.

Round to the Nearest Tenth

The problem requires answers expressed in milliliters to be rounded to the nearest tenth where necessary. The calculated result of 2.8 mL is already rounded to the nearest tenth.

Label the Answer Correctly

Finally, ensure the answer has the correct labeling, which in this case is "mL" since it is a liquid measurement. The dosage required is 2.8 mL.

Key concepts

Medication Dosage Calculation

Calculating medication dosages accurately is crucial for patient safety and effective treatment. One of the most reliable methods for dosage calculation is dimensional analysis. This approach involves converting different units of measurement to find the correct dosage. It helps to ensure that the medication is administered in the correct amount as prescribed, either in milligrams, milliliters, or other units.

When using dimensional analysis, you always start with what you know, and methodically convert to the desired result. For instance, if a physician orders a medication dose in milligrams and you have a supply in milligrams per milliliter, you need to determine how many milliliters should be administered. This requires setting up a ratio or relationship between two fractions, so one unit can be converted to another.

The formula generally takes the form of:

• Ordered dosage / Available dosage = x (amount of solution needed)

By cross-multiplying and solving for the unknown, you can accurately figure out the exact volume of medication required.

Intravenous Medication

Intravenous (IV) medication involves delivering liquid medication directly into a vein, ensuring a fast and effective method to treat critical conditions. One of the main reasons IV medication is used is because it allows for immediate absorption into the bloodstream, which is essential for quick therapeutic effects.

The process requires calculations to make sure the dosage being administered is precise. Unlike medications administered orally, IV medications go directly into the bloodstream, so errors in dosage can lead to serious consequences. This necessitates a precise calculation and doubling-check of these measurements, as well as a proper understanding of how to set up and maintain IV equipment.

Understanding factors like flow rates (usually expressed in mL/hr) and ensuring that the IV solution is compatible with the patient’s condition and other administered drugs is also important. Healthcare professionals need to be proficient in reading labels and solving dosage problems, as medications like Solu-Medrol require exact dosages based on concentration available.

Proportions in Mathematics

Proportions in mathematics are statements that express the equality of two ratios — an essential concept for problem-solving in various fields, including medication dosage calculations. A proportion expresses that two ratios are equivalent, which is the key element used in dimensional analysis for medication calculations.

For healthcare practitioners, understanding how to set up and solve proportions is fundamental. For example, if we know the concentration of a drug and need to determine the amount to administer for a different dosage, proportions can effectively be used to simplify this calculation.

Here's a basic outline of how it works:

• Identify the known ratio, such as drug concentration or dosage per amount of solution.
• Set up the proportion with the unknown variable on one side of the ratio equation.
• Cross-multiply to form an equation that can be solved for the unknown.
• Solve the equation to find the desired value.

This method allows for precise calculations in real-world situations where accuracy is essential, such as determining the correct volume of an intravenous medication.