Problem 17 - Prealgebra

Question

Number of Graduates Suppose \(60 \%\) of the graduating class in a certain high school goes on to college. If 240 students from this graduating class are going on to college, how many students are there in the graduating class?

Step-by-Step Solution

Answer

There are 400 students in the graduating class.

Step 1: Understand the Problem

We need to find the total number of students in the graduating class given that 60% of them go on to college, and 240 students actually go on to college.

Step 2: Set Up an Equation

Let the total number of students in the graduating class be denoted by \( x \). The problem tells us that 60% of these students, which can be written as \( 0.60x \), are going on to college. We know this number is 240: \( 0.60x = 240 \).

Step 3: Solve for the Total Number of Students

To find \( x \), divide both sides of the equation by 0.60: \[ x = \frac{240}{0.60} \] By solving this division, we find the value of \( x \).

Step 4: Perform the Calculation

Calculate \( \frac{240}{0.60} \): \[ \frac{240}{0.60} = 400 \] Thus, the total number of students in the graduating class is 400.

Key Concepts

graduating class

Graduating class refers to the group of students who are finishing their final year at a school or college. This concept often appears in word problems that involve counting, percentages, or other mathematical operations. Understanding the size of a graduating class can help determine college acceptance rates, class rankings, or other statistics related to academic performance. In the given problem, the graduating class is important because it establishes the total number of students from whom we calculate the percentage going on to college. By analyzing how many students progress to higher education, we can infer various factors about the school, such as its academic strength or the aspirations of its students. Recognizing the proportion helps in making informed decisions about educational strategies and investments.

algebra equations

Algebra equations are mathematical statements that use letters to represent unknown numbers or quantities. Solving these equations is a critical skill when tackling percentage word problems, such as the one about the graduating class.Let's delve into the specific equation from our problem. We define the total number of students as \( x \). Knowing that 60% of these students go to college, we write this percentage as a decimal: \( 0.60 \). Our equation becomes:

• \( 0.60x = 240 \)

This equation tells us that 60% of the total number of students equals 240. To find \( x \), or the total number of students, we solve for the unknown by dividing both sides by 0.60:

• \[ x = \frac{240}{0.60} \]

This form of algebraic manipulation helps us isolate the unknown in the equation, revealing the total graduating class size as 400 students. Using algebra in this way allows us to clearly and efficiently solve real-world problems, making it an indispensable tool in problem-solving scenarios.

problem solving steps

Problem solving steps are strategies that help us organize and tackle mathematical problems like percentages or algebra equations efficiently. The key to solving the provided problem involves breaking it down into manageable parts:First, **understanding the problem** is crucial. Know what is given and what needs to be determined. Identify the relationship between the percentage and the number of students going to college.Next, **setting up an equation** represents translating the problem into a mathematical form. Here we used \( 0.60x = 240 \), representing 60% of the graduating class.Then, it's time to **solve for the unknown**. Isolate the unknown by performing mathematical operations to simplify the equation, such as division in our example:

• \( \frac{240}{0.60} = 400 \)

Finally, **perform the calculation** to verify your results and ensure feasibility. By following these steps, we arrive at 400 students, making sure any assumptions or calculations are accurate.These problem-solving steps help ensure accuracy and efficiency in solving percentage word problems like this one.