Question

What is the number of pallets, each with an area of 60 square yards, that would be needed to cover a field that is 3 acres in area? ( 1 acre \(=\) 4,840 square yards)

Short answer

The short answer version: To cover a 3-acre field with pallets that each have an area of 60 square yards, 242 pallets would be needed. This is calculated by first converting the field's area into square yards (3 acres * 4,840 square yards/acre = 14,520 square yards) and then dividing this by the area of each pallet (14,520 square yards / 60 square yards per pallet = 242 pallets).

Step-by-step solution

Convert acres to square yards

We are given the area of the field as 3 acres. To convert it into square yards, we must multiply the area in acres by the conversion factor, which is 4,840 square yards per acre. So, the total area of the field in square yards is: Area (square yards) = Area (acres) * Conversion factor Area (square yards) = 3 acres * 4,840 square yards/acre

Calculate the number of pallets

Now that we have the area of the field in square yards, we will divide it by the area of each pallet (60 square yards) to find out how many pallets are needed to cover the entire field: Number of pallets = Area (square yards) / Area of each pallet (square yards) Number of pallets = (3 acres * 4,840 square yards/acre) / 60 square yards

Solve for the number of pallets

Now, let's solve for the number of pallets required: Number of pallets = (3 * 4,840) / 60 Number of pallets = 14,520 / 60 Number of pallets = 242 Thus, 242 pallets, each with an area of 60 square yards, are needed to cover the field that is 3 acres in area.

Key concepts

Area Conversion

Area conversion is the process of changing measurements from one unit to another. This is essential when solving problems that involve different units, like acres and square yards.
- **Acres**: Commonly used in agriculture and real estate to measure land area. One acre equates to about 4,840 square yards. - **Square Yards**: Useful for smaller areas or when you need more precision. In our problem, converting acres to square yards allows us to use the same unit for all measurements. This simplifies calculations and makes it possible to determine how many pallets are needed to cover the field. By multiplying the number of acres by the conversion factor of 4,840, we compute the field's total area in square yards.

Acres to Square Yards

To convert from acres to square yards, you utilize a set ratio known as a conversion factor. Understanding this is key in many land measurement calculations. Here’s how it works:- **Step-by-Step**: Multiply the amount in acres by the conversion factor (4,840 square yards per acre). This simple multiplication turns our 3 acres into an area measured in square yards:\[3 ext{ acres} \times 4,840 ext{ square yards per acre} = 14,520 ext{ square yards}\]Now, with the area in square yards, you can proceed to solve other related problems, such as calculating how many 60 square yard pallets are needed.

Division in Problem Solving

Division is fundamental in problem-solving, especially when determining how many items fit into a larger area or volume. In this exercise, we need to divide to find how many pallets fit into the field.- **Understanding the Problem**: We have the total field area in square yards and want to know how many pallets can cover that space.- **Step-by-Step**: Divide the total area (14,520 square yards) by the area of one pallet (60 square yards).The division looks like this:\[rac{14,520 ext{ square yards}}{60 ext{ square yards per pallet}} = 242 ext{ pallets}\]This step tells us that 242 pallets are required. Using division, you break down the field's total area into smaller, manageable amounts, showing how mathematics can solve practical, real-world challenges.