Problem 57 - Calculate With Confidence

Question

A vial holds a total of 7.5 milliliters (mL) of medication. If two injections are withdrawn from the vial (1.6 mL and 0.8 mL), how much medication is left in the vial? ___________________________

Step-by-Step Solution

Answer

5.1 mL of medication is left in the vial.

Step 1: Understand the Problem

We are given a vial with a total medication volume of 7.5 mL. Two injections are taken out of the vial, having volumes of 1.6 mL and 0.8 mL respectively. We need to find out how much medication is left in the vial after both withdrawals.

Step 2: Calculate Total Withdrawn

Add the volumes of the two injections to find the total amount of medication withdrawn. \[1.6\, \text{mL} + 0.8\, \text{mL} = 2.4\, \text{mL}\]

Step 3: Subtract from Initial Volume

Subtract the total amount withdrawn from the initial amount of medication in the vial to find out how much medication is left.\[7.5 \, \text{mL} - 2.4 \, \text{mL} = 5.1 \, \text{mL}\]

Step 4: Final Medication Volume

After both withdrawals, the vial contains 5.1 mL of medication.

Key Concepts

Mathematical Problem Solving

Mathematical problem solving is a key skill for tackling various situations, including those involving medication dosages. It begins by understanding the problem at hand. In our example, we are starting with a vial of medication with an initial volume. We have to determine how much medication is left after withdrawing specific amounts for injections.

The problem-solving process often involves:

• Identifying the quantities involved
• Understanding the operations needed (like addition or subtraction)
• Keeping track of measurements to ensure accuracy

By methodically evaluating each step, we can confidently resolve problems such as calculating remaining medication in a vial after withdrawals, as we've done in this example.

Volume Subtraction

Volume subtraction is crucial in dosage calculations to find out how much liquid is left in a container after a portion has been removed. In our scenario, we begin with a total of 7.5 milliliters (mL) of medication. After removing two injections with volumes of 1.6 mL and 0.8 mL, we need to know the remaining quantity.

We approach this by initially summing up the volumes of both withdrawals to determine the total volume removed:

• Total volume withdrawn: \( 1.6 \, \text{mL} + 0.8 \, \text{mL} = 2.4 \, \text{mL} \)

Next, we subtract the total withdrawn volume from the initial volume:

• Final volume remaining: \( 7.5 \, \text{mL} - 2.4 \, \text{mL} = 5.1 \, \text{mL} \)

This straightforward calculation ensures an accurate assessment of the remaining medication.

Metric Units

Understanding metric units is essential for medication dosage calculations. The metric system is based on powers of ten, making it easy to handle conversions and calculations.

In our example, we work exclusively with milliliters (mL), a common metric unit for measuring liquid volume. The simplicity of using metric units lies in their consistent scale, aiding both calculations and comprehension.
Milliliters are particularly useful in medical settings for dosing liquid medications, allowing for precise volume measurements. Each step in mathematical calculations uses these units consistently, ensuring clarity and preventing errors when dealing with quantities.

Step-by-Step Solution

A step-by-step solution helps resolve math problems by breaking them into manageable parts. This method is invaluable in dosage calculations to avoid errors.

Here's how to approach the exercise:

• Step 1: Clarify the given information and identify what's being asked. Recognize the total initial volume and each injection volume.
• Step 2: Sum the volumes of the injections to determine the total amount withdrawn from the vial.
• Step 3: Subtract the total withdrawn volume from the original volume to find the remaining quantity.
• Step 4: Verify your result: The vial now holds 5.1 mL of medication.

Following a structured approach reduces complexity, enhancing understanding and ensuring precision in problem-solving.