Problem 3 - Prealgebra

Question

Solve each problem using the percent equation. 15 is what percent of \(60 ?\)

Step-by-Step Solution

Answer

15 is 25% of 60.

Step 1: Identify Known Values

Identify the given values in the problem: 15 (part) and 60 (whole). We are looking for the percentage.

Step 2: Write the Percent Equation

The percent equation is \( \text{part} = \left(\frac{\text{percent}}{100}\right) \times \text{whole} \). In this problem: \( 15 = \left(\frac{x}{100}\right) \times 60 \).

Step 3: Solve the Equation for Percent

To isolate \(x\) (the percent), rearrange the equation to solve for \(x\): \( x = \frac{15 \times 100}{60} \).

Step 4: Calculate the Percentage

Perform the calculation: \( x = \frac{1500}{60} = 25 \). Thus, 15 is 25\% of 60.

Key Concepts

Solving for Percent

Finding the percent in a problem requires setting up a proportion or an equation where a part is compared to a whole. In our exercise, we are trying to find what percent 15 is of 60.To do this using the percent equation, we set up our formula: - The part is 15 and the whole is 60.- We represent the unknown percent with a variable, often written as \(x\).So, our equation starts as \( 15 = \left( \frac{x}{100} \right) \times 60\). The goal here is to solve for \(x\), which represents the percentage. This demonstrates how you express a portion of a whole as a percent. By rearranging the equation to solve for \(x\), you perform necessary calculations to reveal the percentage.

Part-Whole Relationship

Understanding the part-whole relationship is crucial when dealing with the percent equation. It clarifies how one value (the part) relates to a total value (the whole). - **Part**: The smaller segment of the total or whole amount. In this context, it is the 15 that we are examining. - **Whole**: The total amount from which the part is derived. Here, the whole is 60. This relationship explains that if you know the whole and a given part, you can find what fraction or percent that part is of the whole. By plugging these values into the percent equation, you can determine the percentage. Recognizing this relationship helps make sense of different math problems involving percentages.

Basic Arithmetic Calculations

Arithmetic calculations play a vital role in solving percent problems, allowing you to work through equations step-by-step to find the answer. In our example, this process involves a few key operations:- **Multiplication**: Here, multiplying \(x/100\) by 60 initially helped set up the equation \( 15 = \left( \frac{x}{100} \right) \times 60 \). - **Rearrangement**: Solving for \(x\) requires rearranging the equation to \( x = \frac{15 \times 100}{60} \). - **Division**: Finally, dividing \(1500\) by \(60\) gives the value of \(x\), which is 25.Performing these simple operations helps you effectively utilize the percent equation in solving such problems. Understanding them streamlines the process and ensures accuracy.