A vial contains 100 mg in 4 mL; prescribed dose is 50 mg. How many mL should be drawn?

A vial contains 100 mg in 4 mL; prescribed dose is 50 mg. How many mL should be drawn?

• A. 1 mL
• B. 2 mL
• C. 3 mL
• D. 4 mL

Answer: (B)

The key idea is that dose is proportional to volume when the concentration is fixed. Here, 100 mg are in 4 mL, which means the concentration is 100 mg / 4 mL = 25 mg per mL. To obtain a 50 mg dose, you need 50 mg ÷ 25 mg/mL = 2 mL. Since 50 mg is half of 100 mg, you’re taking half of the 4 mL, which also gives 2 mL. Check: 2 mL × 25 mg/mL = 50 mg. Drawing 1 mL would give 25 mg; 3 mL would give 75 mg; 4 mL would give 100 mg, so 2 mL is the correct amount.

The key idea is that dose is proportional to volume when the concentration is fixed. Here, 100 mg are in 4 mL, which means the concentration is 100 mg / 4 mL = 25 mg per mL. To obtain a 50 mg dose, you need 50 mg ÷ 25 mg/mL = 2 mL. Since 50 mg is half of 100 mg, you’re taking half of the 4 mL, which also gives 2 mL. Check: 2 mL × 25 mg/mL = 50 mg. Drawing 1 mL would give 25 mg; 3 mL would give 75 mg; 4 mL would give 100 mg, so 2 mL is the correct amount.