Question

Set up the following word problems as proportions and solve. Include labels in the set up and on the answer. A tablet (tab) contains 325 milligrams (mg) of medication. How many tabs contain \(975 \mathrm{mg}\) of medication?

Short answer

3 tablets are needed for 975 mg.

Step-by-step solution

Understand the Problem

We've been given a problem about medication in tablets. We're told that one tablet contains 325 mg, and we need to find out how many tablets are required for 975 mg.

Set Up the Proportion

We set up a proportion to compare the known information with the unknown information. The proportion is \( \frac{1 \text{ tablet}}{325 \text{ mg}} = \frac{x \text{ tablets}}{975 \text{ mg}} \), where \( x \) is our unknown number of tablets.

Solve the Proportion

To solve for \( x \), we use cross-multiplication. This gives us the equation \( 1 \times 975 = 325 \times x \). Simplifying, we have \( 975 = 325x \).

Isolate the Variable

We solve for \( x \) by dividing both sides of the equation by 325, resulting in \( x = \frac{975}{325} \).

Calculate the Result

Perform the division \( \frac{975}{325} = 3 \). Therefore, \( x = 3 \).

Label the Answer

We've found that \( x = 3 \text{ tablets} \). This means it will take 3 tablets to contain 975 mg of medication.

Key concepts

Medication Dosage Calculation

Medication dosage calculation is essential for ensuring patients receive the right amount of a drug. Without careful calculation, there is a risk of underdosing or overdosing, which can be dangerous. This process uses simple math to make sure the correct quantity of medication is given based on the instructions or requirements.

Key points to remember when calculating medication dosages:

• Always start by understanding the problem. Know what the total dosage requirement is, and what the strength of the medication you have is.
• Convert any measurements so that they are in the same units if necessary. This prevents errors in calculation.
• Set up a proportion when comparing different strengths and amounts—this is very helpful in finding the missing value, whether it's the amount of medication or the number of pills needed.

These steps ensure a precise calculation and help maintain safe and effective patient care.

Tablet Medication Math

When working with tablet medication math, you are working with a specific type of dosage calculation that involves tablets or pills. This is common in both clinical practice and when patients need to understand their own prescriptions.

To make this math straightforward:

• Identify the dosage per tablet. This is often indicated on the medication bottle or package.
• Identify the total amount of medication prescribed or required.
• Set up a proportion. For example, if one tablet contains 325 mg and the patient needs 975 mg, the equation is set as 1 tab/325 mg = x tabs/975 mg. This helps in finding the exact number of tablets required.
• Use cross-multiplication to find the unknown variable. This is done by multiplying across the equal sign, resulting in a simple equation to solve.

Following these steps, one can quickly determine how many tablets are needed without confusion, ensuring proper adherence to medication advice.

Mathematical Problem Solving

Mathematical problem solving is the process of identifying, understanding, and solving problems using mathematical methods. This involves several strategic steps designed to simplify complex problems.

Here's how you do it:

• Understand the Problem: Recognize all given information and what you need to find. This is crucial to avoid errors from misinterpretation.
• Translate the Problem: Convert the words into a mathematical expression or equation. Use known formulas or create proportions, like in medication dosage scenarios.
• Solve the Equation: Implement strategies such as cross-multiplication or algebraic manipulation to isolate variables and reach a solution.
• Check Your Work: After arriving at a solution, verify by plugging it back into the original equation or context to ensure it correctly solves the problem.

Using this structured approach is helpful not only in medication calculations but in any mathematical challenges, developing both competence and confidence in problem-solving abilities.