Problem 32 - 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 brand of amoxicillin has a dosage strength of 125 \(\mathrm{mg} / 5 \mathrm{mL} .\) If a patient is prescribed a dosage of \(25 \mathrm{mg}\) how many milliliters should she take?

Step-by-Step Solution

Answer

The patient should take 1 milliliter of amoxicillin.

Step 1: Understand the Dosage Strength

The dosage strength given is that 5 milliliters of this amoxicillin brand contains 125 mg of the medication. This means that for every 5 milliliters, there is 125 mg of amoxicillin.

Step 2: Set Up a Proportion

We can set up a proportion to find out how many milliliters correspond to 25 mg of the medication. The proportion is based on the relationship: \( \frac{125 \, \text{mg}}{5 \, \text{mL}} = \frac{25 \, \text{mg}}{x \, \text{mL}} \), where \(x\) is the amount of mL needed.

Step 3: Solve the Proportion

To find \(x\), we cross-multiply the proportion: \(125 \cdot x = 25 \cdot 5\). This results in the equation \(125x = 125\). Divide both sides by 125 to solve for \(x\): \(x = 1\).

Step 4: Interpret the Solution

The solution tells us that the patient should take 1 milliliter of the amoxicillin to receive the prescribed dosage of 25 mg.

Key Concepts

Dosage Calculations

Dosage calculations are crucial in ensuring a patient receives the right amount of medication. When you have a prescription, it often tells you how much of the drug to take, usually in milligrams (mg). However, liquid medications are provided in milliliters (mL).

To find out how much liquid to administer, you need to calculate the correct dosage. For instance, if a medication has a dosage strength of 125 mg per 5 mL, and the prescribed dosage is 25 mg, you need to find out how many milliliters correspond to this prescribed amount.

In this example, you'll use a ratio, comparing the prescribed dosage to the medication's strength. This is called setting up a proportion, which helps in efficiently calculating the amount needed. Knowing this is fundamental to accurately administering medication, ensuring patient safety.

Milliliters Conversion

When dealing with liquid medications, conversion to milliliters is often necessary. A common misunderstanding is that a direct conversion from milligrams to milliliters is possible without additional information. However, you need to know the concentration of the medication.

For example, if a medication's dosage is expressed as 125 mg per 5 mL, it means 5 milliliters of the liquid contains 125 milligrams. When prescribed 25 mg, it becomes essential to convert this to the corresponding volume in milliliters.

• First, understand the concentration given (e.g., 125 mg/5 mL).
• Use this information to establish a proportion based on the required dosage.

Appropriate conversion ensures the patient receives the correct dose, preventing under or overdosing. Efficient conversion practices safeguard both patient health and therapeutic success.

Cross-Multiplication

Cross-multiplication is a powerful technique used to solve proportions, which is fundamental in dosage problems. When you have a proportion like \( \frac{125 \, \text{mg}}{5 \, \text{mL}} = \frac{25 \, \text{mg}}{x \, \text{mL}} \), cross-multiplication becomes your best friend.

Here's how it works:

• Multiply the means (the inside terms), so it's \(25 \times 5\).
• Multiply the extremes (the outer terms), so it's \(125 \times x\).
• Set these two products equal: \(125x = 125\).

Solve for \(x\). In this case, you divide both sides by 125, leading to \(x = 1\). This means 1 mL of the liquid is required for a 25 mg dose.

Using cross-multiplication simplifies proportion problems, making it a straightforward way to find an unknown variable in medication dosage calculations.