Problem 108 - Prealgebra

Question

A fungus called ”white-nose syndrome” has killed an estimated 500,000 bats throughout the country. This means about 2,400,000 pounds of bugs aren’t eaten over the year, says Forest Service biologist Becky Ewing. How many pounds of insects does an average bat eat annually? Associated Press-Times-Standard 5/2/09

Step-by-Step Solution

Answer

Each bat eats 4.8 pounds of insects annually.

Step 1: Understand the Problem

We need to find the average number of pounds of insects that each bat eats annually. We know that the total number of bats is 500,000 and these bats would have collectively eaten 2,400,000 pounds of insects in a year.

Step 2: Set Up the Division Equation

Each bat consumes the same amount of insects annually. To find out how many pounds each bat eats, we divide the total pounds of insects by the total number of bats. This can be represented by the equation: \( \frac{2,400,000}{500,000} \).

Step 3: Perform the Division

Divide 2,400,000 by 500,000 to find out how many pounds each bat eats. This calculation simplifies to: \( \frac{2,400,000}{500,000} = 4.8 \).

Step 4: Interpret the Answer

The result from the division tells us that each bat eats, on average, 4.8 pounds of insects each year.

Key Concepts

Understanding Word Problems

Word problems can often seem daunting, but breaking them down into smaller steps can make the process more manageable. The first key step in understanding a word problem is to read it carefully to grasp what is being asked.
In this specific scenario, the problem talks about the total weight of insects not eaten because of the death of 500,000 bats due to a fungus.
It is crucial to identify the known quantities:

• The total number of bats that died: 500,000.
• The total weight of insects that would have been eaten by these bats: 2,400,000 pounds.

The question asks us to determine the average amount of insects each bat eats in a year. By focusing only on relevant data, we can proceed with solving the problem effectively. Understanding the relationship between these numbers is the foundation for solving the problem.

Simple Division

Once the problem is understood, the next step is to set up a simple division calculation as indicated in the word problem. Division is the process of determining how many times one number is contained within another.
In this case, we use division to find out how many pounds of insects each bat would eat on average. The mathematical operation involves dividing the total pounds of insects (2,400,000) by the number of bats (500,000). This can be expressed in division form as:

• \[ \frac{2,400,000}{500,000} \]

This equation allows us to simplify and find the answer. Division problems like these are about evenly distributing a total amount, in this case, bugs, among a certain number of units, or bats. It's a basic form of calculation, but crucial for understanding averages in everyday word problems.

Problem Solving Steps

Solving word problems involves a series of methodical steps that guide you to the correct answer. Here, we describe those steps in the context of our problem:

• Outline the Problem: Start by identifying what you're being asked. In this problem, it is the average consumption of insects per bat annually.
• Formulate a Plan: Set up a division to find the average. This step translates the word problem into a concrete mathematical operation.
• Execute the Plan: Perform the division operation. Starting with the simplified equation \( \frac{2,400,000}{500,000} \) simplifies directly to 4.8.
• Review the Solution: Finally, interpret the result and ensure it makes sense within the context of the problem. Each bat eating 4.8 pounds of insects annually aligns with the information given initially.

By clearly defining each stage, students can build confidence in their problem-solving skills, fostering a better understanding of how basic arithmetic like division applies in real-world contexts.