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1. If an insulin injection contains 100 units of insulin per milliliter, how many milliliters should be injected to receive 40 units of insulin?

2. An injection contains 2 mg of medication per milliliter (mL). If a physician prescribes a dose of 0.5 mg to be administered to a hospital patient three times daily, how many milliliters of injection will be required over a 5-day period?

3. In a clinical study, a drug produced drowsiness in 30 of the 1500 patients studied. How many patients of a certain pharmacy could expect similar effects, based on a patient count of 100?

4. A formula for 1250 tablets contains 6.25 grams of diazepam. How many grams of diazepam should be used in preparing 550 tablets?

5. If 100 capsules contain 400 mg of an active ingredient, how many milligrams of the ingredient will 48 capsules contain?

6. Each tablet of TYLENOL WITH CODEINE contains 30 mg of codeine phosphate and 300 mg of acetaminophen. By taking 2 tablets daily for a week, how many milligrams of each drug would the patient take?

7. A cough syrup contains 10 mg of dextromethorphan hydrobromide per 5 mL. How many milligrams of the drug are contained in a 120-mL container of the syrup?

8. If an intravenous fluid is adjusted to deliver 15 mg of medication to a patient per hour, how many milligrams of medication are delivered per half minute?

9. The biotechnology drug filgrastim is available in syringes containing 480 micrograms (mcg) of filgrastim per 0.8 mL. How many micrograms of the drug would be administered by each 0.5 mL injection?

10. An oral solution contains, in each milliliter, 80 mg of lopinavir and 20 mg of ritonavir. How many milligrams of each drug would be contained in a calculated dose of 0.4 mL?

Answer :

Sure, let's break down each question step by step:

1. Insulin Injection:
- You need to find how many milliliters (mL) are needed to deliver 40 units of insulin if each milliliter contains 100 units.
- Calculation: [tex]\( \text{milliliters needed} = \frac{40 \text{ units}}{100 \text{ units/mL}} = 0.4 \text{ mL} \)[/tex].

2. Medication Dose Over 5 Days:
- The injection contains 2 mg of medication per mL.
- The prescribed dose is 0.5 mg, three times a day, for 5 days.
- First calculate the total mg needed: [tex]\( 0.5 \times 3 \times 5 = 7.5 \text{ mg} \)[/tex].
- Then, convert mg to mL: [tex]\( \text{milliliters needed} = \frac{7.5 \text{ mg}}{2 \text{ mg/mL}} = 3.75 \text{ mL} \)[/tex].

3. Drowsiness from Medication:
- In a study, 30 out of 1500 patients experienced drowsiness.
- You want to find out how many out of 100 patients could experience drowsiness.
- Find the percentage: [tex]\( \text{percentage} = \frac{30}{1500} \)[/tex].
- Apply that percentage to 100 patients: [tex]\( \frac{30}{1500} \times 100 = 2 \)[/tex] patients.

4. Diazepam for Tablets:
- For 1250 tablets, 6.25 grams of diazepam are used.
- You need to find the grams for 550 tablets.
- First find grams per tablet: [tex]\( \frac{6.25 \text{ grams}}{1250 \text{ tablets}} \)[/tex].
- Then calculate for 550 tablets: [tex]\( \frac{6.25}{1250} \times 550 = 2.75 \text{ grams} \)[/tex].

5. Active Ingredient in Capsules:
- 100 capsules contain 400 mg of an ingredient.
- Find the amount for 48 capsules.
- Find mg per capsule: [tex]\( \frac{400 \text{ mg}}{100} \)[/tex].
- Then calculate for 48 capsules: [tex]\( \frac{400}{100} \times 48 = 192 \text{ mg} \)[/tex].

6. Tylenol with Codeine Tablets:
- Each tablet has 30 mg of codeine and 300 mg of acetaminophen.
- Calculate for 2 tablets daily for a week (7 days).
- For codeine: [tex]\( 30 \text{ mg} \times 2 \times 7 = 420 \text{ mg} \)[/tex].
- For acetaminophen: [tex]\( 300 \text{ mg} \times 2 \times 7 = 4200 \text{ mg} \)[/tex].

7. Cough Syrup Dextromethorphan Content:
- The syrup contains 10 mg of dextromethorphan per 5 mL.
- Calculate the total mg in 120 mL.
- Calculate mg per mL: [tex]\( \frac{10}{5} \)[/tex].
- Total for 120 mL: [tex]\( 2 \times 120 = 240 \text{ mg} \)[/tex].

8. IV Medication Delivery:
- The fluid delivers 15 mg per hour.
- Find mg delivered per half minute (0.5 minute).
- First, find per minute: [tex]\( \frac{15}{60} = 0.25 \text{ mg/minute} \)[/tex].
- Then for half minute: [tex]\( 0.25 \times 0.5 = 0.125 \text{ mg} \)[/tex].

9. Filgrastim in Syringes:
- Syringes contain 480 mcg per 0.8 mL.
- Find mcg per 0.5 mL.
- First find mcg per mL: [tex]\( \frac{480}{0.8} \)[/tex].
- Then calculate for 0.5 mL: [tex]\( 600 \times 0.5 = 300 \text{ mcg} \)[/tex].

10. Lopinavir and Ritonavir in Oral Solution:
- Each mL has 80 mg of lopinavir and 20 mg of ritonavir.
- Calculate for a 0.4 mL dose.
- Lopinavir: [tex]\( 80 \times 0.4 = 32 \text{ mg} \)[/tex].
- Ritonavir: [tex]\( 20 \times 0.4 = 8 \text{ mg} \)[/tex].

These calculations help determine the necessary quantities for accurate dosage and expected outcomes in various scenarios.

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