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Understanding ratio and proportion is essential for pharmacy technicians. These concepts help in accurately calculating medication dosages, compounding medicines, and managing inventory. This article provides practice problems to enhance your skills in ratio and proportion.
Basic Concepts of Ratio and Proportion
A ratio compares two quantities, showing how many times one value contains another. A proportion states that two ratios are equal. Mastering these concepts is vital for precise pharmaceutical calculations.
Practice Problems
Problem 1: Simple Ratio
If the ratio of the number of tablets to capsules is 3:2, and there are 12 tablets, how many capsules are there?
Problem 2: Solving for Unknown in Ratio
The ratio of drug A to drug B is 5:3. If there are 15 units of drug A, how many units of drug B are there?
Problem 3: Proportion in Dosage Calculation
A patient requires a dose of 250 mg, which is 50% of the medication available. How much medication is available?
Problem 4: Mixing Solutions
To prepare a 10% solution, how much of a 20% solution should be mixed with pure water to obtain 200 mL of the 10% solution?
Answers and Explanations
Problem 1: The ratio 3:2 means for every 3 tablets, there are 2 capsules. If 12 tablets are present, then:
Number of capsules = (2/3) × 12 = 8 capsules.
Problem 2: Set up the proportion: 5/3 = 15/x. Cross-multiplied: 5x = 45. Therefore, x = 9 units of drug B.
Problem 3: 50% of the medication equals 250 mg, so the total medication available is:
250 mg / 0.5 = 500 mg.
Problem 4: Let x be the amount of 20% solution used. The amount of pure water added is (200 – x) mL. The mixture equation:
(0.20)x = 0.10 × 200
x = (0.10 × 200) / 0.20 = 100 mL.
So, 100 mL of the 20% solution should be mixed with 100 mL of water to make 200 mL of a 10% solution.