Problem 10 - Prealgebra

Question

Solve each of these problems using the method developed in this section. The enrollment in a certain elementary school was 410 in 2007 . In 2008 , the enrollment in the same school was \(328 .\) Find the percent decrease in enrollment from 2007 to 2008.

Step-by-Step Solution

Answer

The percent decrease in enrollment from 2007 to 2008 is approximately 20%.

Step 1: Identify the Initial and Final Values

The initial enrollment in 2007 is 410 students. The final enrollment in 2008 is 328 students.

Step 2: Determine the Difference in Enrollment

Subtract the final enrollment from the initial enrollment to find the decrease: \( 410 - 328 = 82 \). The enrollment decreased by 82 students.

Step 3: Calculate the Percent Decrease

Use the formula for percent decrease: \( \text{Percent Decrease} = \left(\frac{\text{Decrease in Enrollment}}{\text{Initial Enrollment}}\right) \times 100 \). Plug in the values: \( \left(\frac{82}{410}\right) \times 100 \approx 20\% \).

Key Concepts

What is Enrollment?

Enrollment refers to the total number of students registered at a school or educational institution during a specific period. In this exercise, the term is used to count the number of students attending an elementary school at certain points in time, specifically in the years 2007 and 2008. Enrollment numbers can fluctuate each year due to various factors such as demographic changes, school zoning updates, or even educational policy changes. Monitoring enrollment trends helps schools effectively plan resources like teachers, classrooms, and supplies, ensuring each student receives the attention and education they deserve. By understanding enrollment and its trends, schools can address challenges efficiently and adapt their strategies, keeping the learning environment optimal for all students.

Understanding Elementary School

Elementary school, also known as primary school in some countries, is the foundational stage of formal education that serves children before they enter middle school. Typically, students in elementary schools range from kindergarten through fifth or sixth grade, depending on the educational system in place. The focus in these early years is to build basic academic skills such as reading, writing, and math, while also encouraging the development of social skills and emotional growth. The importance of monitoring enrollment at this level is especially crucial because it directly affects the student-teacher ratio, which influences the quality of education and individual attention each child can receive. Young students thrive in environments where they feel supported and recognized, both academically and socially.

Using a Mathematical Formula for Percent Decrease

Calculating percent decrease is useful to understand how much something has diminished in size or quantity, in relation to its original state. This concept applies to a wide range of situations, including monitoring enrollment changes in schools.To find the percent decrease in enrollment for the given problem, we start by identifying the initial and final values of enrollment:

• Initial enrollment (2007): 410 students
• Final enrollment (2008): 328 students

Next, we determine the difference between these values by subtracting the final enrollment from the initial enrollment:\[ 410 - 328 = 82 \]This means there was a decrease of 82 students. To calculate the percent decrease, we use the mathematical formula:\[ \text{Percent Decrease} = \left(\frac{\text{Decrease in Enrollment}}{\text{Initial Enrollment}}\right) \times 100 \]Plugging in the values, the calculation is:\[ \left(\frac{82}{410}\right) \times 100 \approx 20\% \]This tells us that the enrollment decreased by approximately 20% from 2007 to 2008. Understanding this calculation helps in assessing and addressing the changes within the institution effectively.