Problem 102 - Prealgebra

Question

Using the 2008 Ohio Farm Custom Rates, the average cost for spreading dry bulk fertilizer is about \(\$ 4.50\) per acrè. What is the c?st to fertilizè 50 acrees?

Step-by-Step Solution

Answer

The cost to fertilize 50 acres is \( \$225 \).

Step 1: Identify the Variables

First, let's identify the information given in the question. The cost to spread fertilizer per acre is \( \$4.50 \) and the number of acres is 50.

Step 2: Set Up the Equation

We can set up the equation to find the total cost by multiplying the cost per acre by the number of acres:\[ \text{Total Cost} = \text{Cost per Acre} \times \text{Number of Acres} \]

Step 3: Substitute the Values

To find the total cost, substitute the known values into the equation:\[ \text{Total Cost} = 4.50 \times 50 \]

Step 4: Calculate the Total Cost

Multiply \( 4.50 \) by \( 50 \) to calculate the total cost:\[ \text{Total Cost} = 225 \]

Step 5: Interpret the Result

The total cost to fertilize 50 acres is \( \$225 \).

Key Concepts

Multiplication

In prealgebra, understanding multiplication is crucial as it forms the foundation for many mathematical concepts. Here, multiplication is used to determine the total cost of fertilizer needed for a certain number of acres. Think of multiplication as repeated addition. For example, multiplying the cost of fertilizing an acre by the number of acres is like adding the same cost several times. In this exercise, we multiply the cost per acre (\(\\(4.50\)) by the number of acres (50). This gives us the total cost:- Cost for 1 acre: \(\\)4.50\)- Cost for 50 acres: \(4.50 \times 50\)Remember, multiplication is not just about numbers but also helps in organizing and understanding real-world problems like this one.

Unit Cost Calculation

Unit cost calculation is a fundamental concept in prealgebra, especially useful in determining expenses over a quantity of items or area, like in farming or shopping. The 'unit cost' is the cost for a single unit of product or service. Here, the unit cost is the expense to fertilize one acre, which is \(\\(4.50\).To find the total cost for multiple units, simply multiply the unit cost by the total number of units. In this example:- Unit cost per acre: \(\\)4.50\)- Total number of acres: 50By determining the unit cost first, you can easily scale up to find totals for any number, making it an invaluable tool for budget planning and price comparisons.

Step-by-Step Math Solution

A step-by-step math solution is essential for breaking down complex problems into manageable steps, especially for students new to prealgebra.1. **Identify the variables**: Recognize what information is provided. In this exercise, we have the cost per acre and the total acres. 2. **Set up the equation**: Plan how to solve it by deciding on an equation. Here, we use: \[ \text{Total Cost} = \text{Cost per Acre} \times \text{Number of Acres} \]3. **Substitute the values**: Replace the variables in your equation with the numbers given in the problem: \[ \text{Total Cost} = 4.50 \times 50 \]4. **Calculate**: Perform the multiplication to find the answer, which is \(\$225\). This shows the complete process for calculating the result, ensuring understanding and accuracy.By following these steps, students can solve similar problems effectively, building confidence in their math skills.