DrugI I available in plain, uncoated tablets containing 75 mg. The weight of these tablets was determined to be 157.5 mg each. Explain how the quantity of DrugI required for the following prescription can be obtained using the minimum number of tablets.
Rx	DrugI	5 mg
 	Lactose ad	300 mg
 	Prepare 36 such capsules	 
Sig	One cap. 2 X a day

To determine how to obtain the required quantity of **DrugI** using the minimum number of tablets, let's break the problem down step by step:

### Step 1: Understand the prescription
- The prescription requires 5 mg of **DrugI** per capsule.
- You need to prepare 36 capsules, so the total quantity of **DrugI** required is:

\[
5 \, \text{mg/capsule} \times 36 \, \text{capsules} = 180 \, \text{mg of DrugI}.
\]

### Step 2: Determine the amount of **DrugI** per tablet
- Each tablet contains 75 mg of **DrugI** and weighs 157.5 mg.
- Thus, 75 mg of the 157.5 mg tablet mass is **DrugI**, and the remaining mass (157.5 mg - 75 mg = 82.5 mg) consists of excipients (inactive substances, like binders).

### Step 3: Calculate the number of tablets required
To get 180 mg of **DrugI**, you divide the required amount by the amount of **DrugI** per tablet:

\[
\frac{180 \, \text{mg of DrugI}}{75 \, \text{mg/tablet}} = 2.4 \, \text{tablets}.
\]

Since you can't use a fraction of a tablet when working practically, you would need to round **up** to the next whole number, which is **3 tablets**.

### Step 4: How to use these 3 tablets
The total weight of 3 tablets would be:

\[
157.5 \, \text{mg/tablet} \times 3 = 472.5 \, \text{mg}.
\]

From these 3 tablets, the total amount of **DrugI** is:

\[
75 \, \text{mg/tablet} \times 3 = 225 \, \text{mg of DrugI}.
\]

You only need 180 mg of **DrugI**, so you will have an excess of:

\[
225 \, \text{mg} - 180 \, \text{mg} = 45 \, \text{mg}.
\]

### Step 5: How to adjust for the excess amount
Since you will have 45 mg extra **DrugI**, you need to account for this in the preparation of the capsules. You can mix the tablet powder (which includes both **DrugI** and the inactive excipients) with **lactose** to reach the desired weight per capsule, adjusting the amount of lactose to compensate for the excess **DrugI**.

### Final Summary:
- Use 3 tablets to obtain the required amount of **DrugI**.
- From these 3 tablets, you will get 225 mg of **DrugI**, but you only need 180 mg.
- Adjust the mixture with lactose to make sure each capsule has the correct dosage of **DrugI**.

Would you like further details or have any questions about this process?

Here are 5 related questions for further exploration:
1. How would you adjust the amount of lactose if the excess **DrugI** was significantly larger?
2. What would happen if you used only 2 tablets instead of 3? Would you be short of **DrugI**?
3. Can you explain why rounding up tablets is important in this case?
4. How would the calculation change if each tablet had a different concentration of **DrugI**?
5. How could you accurately weigh and divide the tablets if fractional doses were required?

**Tip**: Always calculate the total active ingredient needed before deciding on how many tablets to use, and ensure you account for excipients when adjusting the final dosage.

DrugI I available in plain, uncoated tablets containing 75 mg. The weight of these tablets was determined to be 157.5 mg each. Explain how the quantity of DrugI required for the following prescription can be obtained using the minimum number of tablets. Rx DrugI 5 mg, Lactose ad 300 mg, Prepare 36 such capsules, Sig One cap. 2 X a day.

Learn how to calculate the minimum number of DrugI tablets needed to prepare 36 capsules with 5 mg of DrugI per capsule. This problem involves key concepts such as proportions, rounding, and basic arithmetic. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation