Problem 31 - Prealgebra

Question

Nursing Liquid medication is usually given in milligrams per milliliter. Use the information to find the amount a patient should take for a prescribe dosage. A patient is prescribed a dosage of Ceclor" of \(561 \mathrm{mg}\). The dosage strength is 187 mg per 5 mL. How many milliliters should he take?

Step-by-Step Solution

Answer

The patient should take 15 mL.

Step 1: Understand the Given Information

The given problem states that a patient needs to take a dosage of 561 mg. The dosage strength provided is 187 mg per 5 mL.

Step 2: Set Up the Proportion

To calculate how many milliliters correspond to 561 mg, set up a proportion: \( \frac{187 \text{ mg}}{5 \text{ mL}} = \frac{561 \text{ mg}}{x \text{ mL}} \). This proportion relates the given strength to the required dosage.

Step 3: Solve for x

Cross-multiply the proportion to solve for \(x\). We get: \( 187x = 561 \times 5 \).

Step 4: Calculate the Cross-Multiplication

Compute the right side: \( 561 \times 5 = 2805 \). So the equation becomes: \( 187x = 2805 \).

Step 5: Isolate x

Divide both sides by 187 to find \(x\): \( x = \frac{2805}{187} \).

Step 6: Perform the Division

Divide 2805 by 187 to get the number of milliliters: \( x \approx 15 \) mL.

Key Concepts

Dosage Calculation

Dosage calculation is a key skill, especially in areas like nursing and pharmacology. When medical professionals calculate dosages, they ensure patients receive the correct amount of medication for optimal treatment. In the context of this exercise, the objective is to find the equivalent volume in milliliters that corresponds to a given dose in milligrams.

To start, it's crucial to understand the given values: the prescribed dosage (in mg) and the dosage strength (mg per mL). Here, a prescription indicates a dosage of 561 mg of Ceclor®, and the medication’s strength is 187 mg for every 5 mL. Calculating the correct mL intake using these figures helps patients receive an efficient and safe amount of medication.

Cross-Multiplication

Cross-multiplication is a mathematical technique used to solve proportions. A proportion is an equation that states two ratios are equal. In dosage calculations, these ratios often relate the amount of medication to its volume.

To solve a dosage problem, set up a proportion based on the available information. For example, with 187 mg corresponding to 5 mL, and you need to find out how many mL for 561 mg. Write this as a ratio:

• \( \frac{187 \text{ mg}}{5 \text{ mL}} = \frac{561 \text{ mg}}{x \text{ mL}} \)

Cross-multiply to find \( x \), the unknown volume in milliliters. Multiply across the equals sign:

• \( 187x = 561 \times 5 \)

Ultimately, this helps in isolating \( x \) and solving for it by dividing by the coefficient of \( x \), ensuring accurate dosage delivery.

Unit Conversion

Unit conversion involves changing one unit of measurement to another. In healthcare, correct unit conversion is vital for safe medication administration. Many medications are expressed in milligrams (mg) for total dose but prescribed by volume in milliliters (mL).

Understanding unit conversion is essential. The challenge often lies in linking medication dose (mg) to its liquid volume (mL). By setting a clear proportion, such as the relationship of 187 mg to 5 mL, you can utilize cross-multiplication to seamlessly convert units, ensuring that the patient's prescribed dose correlates directly to the liquid volume they intake.

Medication Measurement

Medication measurement is crucial for patient safety and treatment efficacy. Accurate measurement ensures patients receive the dose doctors prescribed without error. When measuring liquid medication, nurses and pharmacists rely on specific ratios to match the prescription to the liquid dose.

In this exercise, you know that 561 mg is needed. With the strength given as 187 mg per 5 mL, correct steps, including setting up a proportion and using cross-multiplication, enable precise calculations. This assures that the patient receives precisely 15 mL, as calculated, to meet the established dosage requirements. Such careful measurement keeps medication administration safe and effective.