Problem 101 - Prealgebra

Question

In Napa Valley, one acre of good land can produce about \(3.5\) tons of quality grapes. At an average price of \(\$ 3,414\) per ton for premium cabernet, how much money could you generate on one acre of cabernet farming? Associated Press-Times-Standard 03/11/10 Grape moth threatens Napa Valley growing method.

Step-by-Step Solution

Answer

The revenue is $11,949 per acre.

Step 1: Identify Given Values

Identify the given values from the problem. We know that one acre of land produces \(3.5\) tons of grapes. The price for each ton of grapes is \(\$3,414\).

Step 2: Establish Revenue Formula

The revenue generated is calculated by multiplying the number of tons produced by the price per ton. The formula is: \( \text{Revenue} = \text{Tons of Grapes} \times \text{Price per Ton} \).

Step 3: Substitute Values into Formula

Substitute the given values into the revenue formula: \( \text{Revenue} = 3.5 \times 3,414 \).

Step 4: Calculate Total Revenue

Perform the multiplication to find the total revenue: \( 3.5 \times 3,414 = 11,949 \). This is the total revenue generated from one acre of cabernet farming.

Key Concepts

Multiplication

Multiplication is a fundamental mathematical operation that comes in handy when solving various everyday problems. In this exercise, multiplication helps us calculate the product of two numbers: the number of tons and the price per ton. By multiplying these values, we find out the potential revenue from one acre of grape farming.

Let's break down the multiplication process for clarity:

• First, identify your two numbers: here, these are 3.5 tons and $3,414 per ton.
• Next, arrange the multiplication: \(3.5 \times 3,414\).
• Perform the multiplication: multiply 3.5 by each digit in 3,414.
• Add up the partial results to find the total.
• The multiplication of simplifications can make solving word problems faster and less prone to error.

Multiplication helps not just in finance or business but also in daily activities like cooking (e.g., scaling recipes) and shopping discounts.

Word Problems

Word problems can seem tricky at first, but they actually help us apply math to real-life scenarios. Solving word problems involves reading carefully, identifying the relevant information, and performing calculations based on that information.

Here's a simple approach to tackle word problems efficiently:

• Read the problem thoroughly to understand the situation it describes.
• Identify the key numbers and units involved.
• Determine what the problem is asking you to find.
• Create a strategy or formula using the given information.
• Solve step-by-step, double-checking your calculations.

For instance, in the cabernet farming word problem, you start by understanding the relationship between the yield per acre and the price per ton. By following these steps, you'll simplify the problem-solving process. Remember, practice makes perfect, so keep working on various word problems to build confidence.

Agricultural Math

Agricultural math combines farming with important calculations, making it an essential tool for farmers. It's used to evaluate crop yields, manage farm resources, and maximize profits. In the context of this exercise, agricultural math helps determine the potential revenue from growing grapes.

Let's emphasize the practical applications of agricultural math:

• Calculate crop yields: Farmers estimate how much produce they can expect from their land.
• Assess profitability: By understanding crop pricing and yields, farmers can forecast profits.
• Resource management: Optimizing the use of water, land, and fertilizers boosts efficiency and sustainability.

Agricultural math enables farmers to make informed decisions about planting, harvesting, and selling crops. It turns abstract numbers into crucial data that influence farming strategies. This exercise demonstrates its importance in determining revenue per acre when farming cabernet grapes. Applying these calculations can improve a farmer's financial strategy and success in the agricultural sector.