Problem 103 - Prealgebra

Question

Huge corporate agribarns house 1000 pigs each. a) If each pig weighs approximately 100 pounds, how many pounds of pig is in each warehouse? b) At an average \(\$ 1.29\) per pound, what is the total cash value for a corporate agribarn? Associated Press-TimesStandard 12/29/09 Pressure rises to stop antibiotics in agriculture.

Step-by-Step Solution

Answer

a) 100,000 pounds; b) USD 129,000.

Step 1: Understanding the Problem

We know from the problem statement that a corporate agribarn houses 1,000 pigs, and each pig weighs approximately 100 pounds. We need to find the total weight in pounds of pigs in each agribarn.

Step 2: Calculating the Total Weight of Pigs

To find the total weight, multiply the number of pigs by the weight of each pig. Since there are 1,000 pigs and each weighs 100 pounds, \[ \text{Total weight} = 1000 \text{ pigs} \times 100 \text{ pounds/pig} = 100,000 \text{ pounds} \]

Step 3: Finding the Cash Value per Pound

Next, we need to calculate the total cash value of the pigs if each pound is worth $1.29. Multiply the total weight of pigs by the price per pound. \[ \text{Total cash value} = 100,000 \text{ pounds} \times USD 1.29/\text{pound} = USD 129,000 \]

Step 4: Verifying Correctness of Calculation

We multiply the components carefully. The calculation of total weight is correct and the cash value is consistent with the weight being multiplied by the price per pound. Hence, both calculations are verified.

Key Concepts

Understanding Problem Statements

In prealgebra problem solving, the first step is to make sure you understand the problem statement thoroughly. This means identifying the key pieces of information given in the problem. In our exercise, we know that a corporate agribarn contains 1,000 pigs. It is also mentioned that each pig weighs approximately 100 pounds. Understanding the statement well allows you to set up your calculations correctly. Always pay attention to details like units and quantities. Highlighting and summarizing the problem in your own words can help. You need to translate the text of the problem into mathematical expressions or steps. Think about what the exercise wants you to find out.

Weight Calculations

Weight calculations are common in different types of math problems. The key is to find the total weight by multiplying the number of items by the weight of one item. Let's apply this to the exercise, where we have 1,000 pigs, each weighing 100 pounds. The calculation for the total weight is straightforward:

• Identify the number of pigs: 1,000.
• Identify the weight per pig: 100 pounds.
• Multiply the two numbers: \[ ext{Total weight} = 1000 \times 100 = 100,000 \text{ pounds} \]

Weight calculations can often involve large numbers. Therefore, double-checking your work by redoing the multiplication is a good habit to get into. Break down the process into smaller parts if needed to avoid mistakes.

Basic Arithmetic Operations

Basic arithmetic operations, such as multiplication and addition, are building blocks in solving many math problems. In our exercise, multiplication is used to find both the total weight of the pigs and the total cash value of the pigs in a warehouse. Once we know the total weight, we ask how much that weight is worth.

• Total weight of pigs: 100,000 pounds.
• Price per pound: \(1.29\text{ USD/pound}\).
• Calculate total cash value: \[ ext{Total cash value} = 100,000 \times 1.29 = 129,000 \text{ USD} \]

In this exercise, notice how multiplication is used to scale up from a simple unit (one pig or one pound) to the totals for larger quantities. Such operations are indispensable in everyday calculations, and practicing them with real-world scenarios helps build a robust understanding.