Problem 45 - Prealgebra

Question

Dilatrate \(^{\circ}-\mathrm{SR}\) comes in 40 milligram capsules. Use this information to determine how many capsules should be given for the prescribed dosages. a. \(120 \mathrm{mg}\) b. 40 mg c. 80 mg

Step-by-Step Solution

Answer

3 capsules for 120 mg, 1 capsule for 40 mg, and 2 capsules for 80 mg.

Step 1: Determine the number of capsules for 120 mg

To find out how many 40 mg capsules are needed for a 120 mg dosage, we divide the total desired dosage by the strength of one capsule. Calculate: \[\frac{120 \text{ mg}}{40 \text{ mg/capsule}} = 3 \text{ capsules}\]

Step 2: Determine the number of capsules for 40 mg

Since 40 mg is the exact dosage of one capsule, you only need 1 capsule.Thus: \[\frac{40 \text{ mg}}{40 \text{ mg/capsule}} = 1 \text{ capsule}\]

Step 3: Determine the number of capsules for 80 mg

To find out how many 40 mg capsules are needed for an 80 mg dosage, divide the total dosage by the amount per capsule. Calculate: \[\frac{80 \text{ mg}}{40 \text{ mg/capsule}} = 2 \text{ capsules}\]

Key Concepts

Dosage Calculation

Dosage calculation is a critical skill in medication management. The primary goal is to ensure that the patient receives the correct amount of medication for their specific needs. When we talk about dosage, we're referring to the specific amount of medication a patient must take. Knowing how to calculate this amount correctly is vital for safety and efficacy.
In our exercise, we calculate the dosage based on the strength of Dilatrate capsules, which are 40 mg each. We need to determine how many capsules are required for different prescribed dosages. Here's how we can think about it:

• First, understand the target dosage your patient needs, for example, 120 mg, 40 mg, or 80 mg.
• Next, divide this target dosage by the strength of one capsule (40 mg in this case).

This simple division helps ensure the correct dosage amount is administered, avoiding over- or under-dosing.

Unit Conversion

Unit conversion plays a crucial role in many dosage calculations. It helps in converting one unit of measure to another to facilitate comparison and ensure accuracy. In the context of medication, these units are often milligrams (mg) or grams (g). Understanding these conversions is essential, as medication instructions may not always match the specific dosage forms available. While our exercise involves straightforward conversions, it demonstrates the importance of ensuring that the numbers match the relevant units. For instance, if medication strength is expressed in mg, make sure dosages are also calculated in mg. Some typical conversions to remember include:

• 1 gram = 1000 milligrams

Unit conversion ensures consistent calculations and helps avoid potential errors related to incompatible units.

Division Problems

Division problems are fundamental in dosage calculations, especially when dividing the total prescribed amount by the per-unit measurement allows us to determine the number of units needed. It simplifies the process of calculating how much medication to prepare or administer.When dealing with dosage calculations, consider the following steps:

• Identify the total dosage required.
• Know the value of each individual unit (in this case, the mg/capsule).
• Divide the total dosage by this unit measurement.

For example, for a 120 mg desired dosage, calculate:\[\frac{120 \text{ mg}}{40 \text{ mg/capsule}} = 3 \text{ capsules}\]This type of division problem is a key part of not just medical but also everyday math, enhancing our ability to allocate resources efficiently.