Problem 52 - Prealgebra

Question

The Google Earth image shows a corn field. A farmer harvests \(29,952\) bushels of com. If the farmer harvested 130 bushels per acre, how many acres does the field cover? (THE IMAGES CANNOT COPY)

Step-by-Step Solution

Answer

The field covers approximately 230 acres.

Step 1: Identify the Formula for the Problem

To determine how many acres the corn field covers, use the formula for total bushels: \( \text{Total Bushels} = \text{Bushels per Acre} \times \text{Acres} \).

Step 2: Rearrange the Formula to Solve for Acres

Rearrange the formula to solve for acres: \( \text{Acres} = \frac{\text{Total Bushels}}{\text{Bushels per Acre}} \).

Step 3: Plug in the Given Values

We know from the problem that the total bushels is \( 29,952 \) and the bushels per acre is \( 130 \). Substitute these values into the formula: \( \text{Acres} = \frac{29,952}{130} \).

Step 4: Calculate the Number of Acres

Calculate the value: \[ \text{Acres} = \frac{29,952}{130} \approx 230.4 \] acres.

Step 5: Round to the Nearest Whole Number (If Required)

Since acres are typically reported as whole numbers in this context, round 230.4 to the nearest whole number to get 230 acres.

Key Concepts

Basic Arithmetic Operations

In prealgebra, basic arithmetic operations are foundational. They include addition, subtraction, multiplication, and division. These operations allow us to solve a variety of mathematical problems. When dealing with word problems, it's important to discern which operation to use. In our exercise, determining how many acres a cornfield covers involves using division.

The arithmetic operation used here—division—requires us to divide the total number of bushels by the number of bushels harvested per acre. This helps us find out how many total acres were covered. It's crucial to be comfortable with these operations as they're used in various real-world calculations, including budgeting and resource management.

Unit Conversion

Unit conversion is the process of converting one type of unit into another. In our exercise, we're given bushels and acres. While we don't need to convert between different units in this specific problem, understanding unit conversion is vital.

In scenarios where different units are involved, like converting kilometers to miles or pounds to kilograms, the principle becomes essential. This skill helps manage situations where units differ, ensuring consistency in calculations. Having a solid grasp on unit conversion can also prevent errors in word problems that involve multiple units.

Algebraic Expressions

Algebraic expressions are crucial for representing mathematical relationships. They allow us to insert, manipulate, and solve equations. In this exercise, we use an algebraic expression to find the number of acres by rearranging the formula for total bushels:

• Total Bushels = Bushels per Acre × Acres
• A resarranged equation: Acres = \(\frac{\text{Total Bushels}}{\text{Bushels per Acre}}\)

Using algebra, we solved for acres. Algebraic expressions help in organizing the terms systematically and changing the subject of the formula. They are key in transitioning from words to meaningful numbers in math problems.

Mastering these expressions makes solving prealgebra problems straightforward, as seen in our effort to calculate the number of acres in the field. This skill is applicable not just in academics but in many practical applications such as economics, engineering, and technology.