Problem 54 - Calculate With Confidence

Question

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

Step-by-Step Solution

Answer

5 tablets were given to the client.

Step 1: Understand the Problem

The client received a total of 17.5 mg of medication. Each tablet contains 3.5 mg. We need to find out how many tablets were given to the client.

Step 2: Set Up the Equation

Let the number of tablets be represented by the variable \( x \). According to the problem, each tablet contains 3.5 mg of medication. We can create the equation: \( 3.5x = 17.5 \).

Step 3: Solve the Equation

To find \( x \), divide both sides of the equation by 3.5: \( x = \frac{17.5}{3.5} \).

Step 4: Calculate the Division

Perform the division: \( x = 17.5 \div 3.5 = 5 \).

Step 5: Interpret the Result

The solution tells us that the number of tablets given to the client is 5.

Key Concepts

Equation Solving

Equation solving is a fundamental part of mathematics where we find the value of a variable that makes the equation true. In our medication dosage problem, step by step, we set up an equation that helps us find the number of tablets given to the client. Let's dive in.

• First, we identify what we need to find. Here, it’s the number of tablets, so we represent it with a variable, like \( x \).
• The problem states that each tablet contains 3.5 mg of medication. This means if we have \( x \) number of tablets, they collectively contain \( 3.5x \) mg of medication.
• We know the total amount of medication given was 17.5 mg. Therefore, the equation that represents this situation is \( 3.5x = 17.5 \).

By arranging these components into an equation, we can proceed to the next step, which is finding the value of \( x \) that satisfies this equation.

Division in Mathematics

Division is a mathematical operation where a number, known as the dividend, is separated into equal parts by another number, known as the divisor. In our problem, we use division to find how many tablets were taken.

• Once we have the equation \( 3.5x = 17.5 \), we need to isolate \( x \) to find how many tablets the client received.
• We do this by performing division: divide both sides of the equation by 3.5. This will cancel out the 3.5 on the left, leaving us with \( x \) on one side of the equation.
• Mathematically, it looks like this: \( x = \frac{17.5}{3.5} \). When we calculate, \( 17.5 \div 3.5 \) equals 5. This shows that \( x \), or the number of tablets, is 5.

Division helps us simplify the problem and determine the value of unknowns. It’s a crucial tool in solving equations, especially in word problems.

Understanding Word Problems

Word problems can sometimes be daunting, but understanding how to break them down makes them manageable and even fun. Let's look at how to tackle them effectively.

• First, read the problem thoroughly to understand what is being asked. Identify the known quantities and unknowns. In our case, we know the total medication and the amount per tablet but not the number of tablets.
• Convert the words into a mathematical model or equation. This often involves identifying relationships between quantities. Here, it was identifying the relationship between the number of tablets and the total medication.
• Use logical steps to solve the equation. Once you’ve set up the equation, use appropriate mathematical operations to find the solution.
• Finally, interpret the result in the context of the problem to ensure it makes sense. Once we found \( x = 5 \), we recognize that 5 tablets provide the required dosage of 17.5 mg.

Learning to navigate word problems boils down to practice and breaking problems into smaller, more manageable parts. This key skill extends beyond math and into real-life problem-solving situations.