Question

A client received 17.5 milligrams (mg) of a medication in tablet form. Each tablet contained \(3.5 \mathrm{mg}\) of medication. How many tablets were given to the client? ______

Short answer

The client was given 5 tablets.

Step-by-step solution

Understand the Problem

Read the problem carefully. You are given a total amount of medication ( 17.5 mg) that the client received and the amount of medication in each tablet (3.5 mg). You need to find out how many tablets make up 17.5 mg.

Set Up the Equation

To find the number of tablets, you can set up the equation as follows: \[ \text{Number of tablets} \times 3.5 = 17.5 \]This equation represents the total medication given.

Solve for the Number of Tablets

Solve the equation from Step 2 to find the number of tablets. Divide both sides of the equation by 3.5 to isolate the number of tablets:\[ \text{Number of tablets} = \frac{17.5}{3.5} \]

Calculate the Result

Perform the division:\[ \frac{17.5}{3.5} = 5 \]So, the number of tablets given to the client is 5.

Key concepts

Mathematical Problem Solving

Mathematical problem solving involves identifying what you know and what you need to find out. In this exercise, it's crucial to extract key details such as the total medication received (17.5 mg) and the medication content per tablet (3.5 mg). Recognizing these values allows us to determine the unknown, which is the number of tablets given.

Start by understanding the relationship between these numbers. Realize that the total medication can be expressed as the product of two quantities: the dosage per tablet and the number of tablets. This helps in forming a mathematical equation to solve the problem. Often, breaking down the problem into smaller segments makes it easier to tackle.

Key aspects include ensuring calculations are logical and precise. Checking your work regularly throughout the process can prevent simple arithmetic errors. Developing a habit of creating equations from word problems is a crucial skill in both mathematics and real-world scenarios, such as medication dosage calculations.

Unit Conversion in Medication

Unit conversion in medication is vital to ensure the patient receives the correct dosage. In this problem, everything is already given in the same units, milligrams (mg), which simplifies the task. However, being familiar with unit conversions is fundamental, as real-world problems often require converting between units.

For example, a doctor might prescribe a medication in grams, and you might have tablets described in milligrams. In such cases, you should know:

• 1 gram (g) = 1000 milligrams (mg)

This knowledge enables you to adjust the values accordingly and make accurate calculations.

Since consistency in units is a must for precise results, always double-check your units before proceeding with your calculations. Not doing so could lead to significant errors in calculations and potential risks for patients in medical contexts.

Equation Solving for Dosage Calculation

Equation solving is a crucial skill when it comes to dosage calculations. It helps in finding unknown quantities effectively. For this exercise, the equation is set as:\[ \text{Number of tablets} \times 3.5 = 17.5 \]This equation reflects the relationship where multiplying the dosage of one tablet by the number of tablets gives the total dosage received. To solve this equation, we isolate the unknown variable, which represents the number of tablets.

For a solution, perform a division:\[ \text{Number of tablets} = \frac{17.5}{3.5} \]This step involves dividing the total dosage by the dosage per tablet.

The calculation yields 5, indicating that the client received 5 tablets. This straightforward approach using basic arithmetic and algebra emphasizes the importance of understanding equations in dosage calculations, ensuring the right amount of medication is administered efficiently.