Problem 68 - Elementary and Intermediate Algebra

Question

During the first two weeks of the semester, 5 students withdrew from Meghan's algebra class, 8 students were added to the class, and 4 students were dropped as "no-shows." By how many students did the original class size change?

Step-by-Step Solution

Answer

The original class size decreased by 1 student.

Step 1 - Identify the Changes

List the changes in the class size. 5 students withdrew, 8 students were added, and 4 students were dropped as 'no-shows'.

Step 2 - Calculate the Total Decrease

Add the number of students who withdrew and the number who were dropped as 'no-shows'. Number of students who left: 5 + 4 = 9

Step 3 - Calculate the Total Increase

Identify the number of students who were added to the class.Number of students added: 8

Step 4 - Determine the Net Change

Subtract the total decrease from the total increase to find the net change in class size. Net Change: 8 - 9 = -1

Key Concepts

Addition and Subtraction in Word Problems

Understanding word problems is crucial because they help us apply math in real-life situations. In word problems related to addition and subtraction, the key is to identify quantities that are being combined or separated. For example, the problem states that 5 students withdrew, 8 students were added, and 4 students were dropped as 'no-shows.' Here, we need to add and subtract these numbers to find the total change. Addition is used when students are added, and subtraction is used when students leave or are dropped. The equation forms the basis for solving addition and subtraction word problems. Break down the problem into smaller, manageable steps for better understanding.

Net Change Calculation

The net change gives us a clear understanding of the overall impact of different actions. To find the net change, consider both the increases and decreases together.

In the given problem:

• 5 students withdrew (decrease)
• 8 students were added (increase)
• 4 students were dropped as 'no-shows' (decrease)

First, we need to calculate the total decrease, which is the sum of students who withdrew and were dropped as 'no-shows': \[5 + 4 = 9\].
Then, we calculate the total increase:\[8\].
The net change is then found by subtracting the total decrease from the total increase: \[8 - 9 = -1\].
This result of -1 indicates that there is an overall decrease in the class size by 1 student.

Problem-Solving Steps

Solving word problems can be easier if you follow systematic steps. Let's break down the example problem into clear steps.

• Step 1: Identify the Changes: List out the numbers of students involved in each action. Here, 5 withdrew, 8 were added, and 4 were dropped as 'no-shows.'
• Step 2: Calculate the Total Decrease: Add the students who withdrew to those dropped as 'no-shows': \[5 + 4 = 9\].
• Step 3: Calculate the Total Increase: Identify the number of students added: \[8\].
• Step 4: Determine the Net Change: Subtract the total decrease from the total increase to find the net change: \[8 - 9 = -1\]. This means the class size decreased by 1 student overall.

This approach ensures that each step is clear and concise, making it easier to solve even complex word problems.