Calculating Average Corn Production per Acre

Oct 13, 2025 by miodeya.com 118 views

Understanding the Problem

In this problem, we are given the total area of Nelly's farmland in acres and the total amount of corn produced each year in bushels. We need to find the average amount of corn produced per acre. This requires us to divide the total amount of corn produced by the total area of the farmland.

Given Information

Total area of farmland: $$4.2 \times 10^2$$ acres
Total amount of corn produced each year: $$6.72 \times 10^4$$ bushels

Calculating Average Corn Production per Acre

To find the average amount of corn produced per acre, we need to divide the total amount of corn produced by the total area of the farmland.

Average corn production per acre = Total amount of corn produced / Total area of farmland

We can represent this mathematically as:

\text{Average corn production per acre} = \frac{6.72 \times 10^4}{4.2 \times 10^2}

Simplifying the Expression

To simplify the expression, we can divide the numerator and denominator by their greatest common factor, which is $$10^2$$.

\text{Average corn production per acre} = \frac{6.72 \times 10^2}{4.2}

Evaluating the Expression

Now, we can evaluate the expression by dividing $$6.72$$ by $$4.2$$.

\text{Average corn production per acre} = 1.6 \times 10^2

Representing the Answer

The average amount of corn produced per acre is $$1.6 \times 10^2$$ bushels.

Conclusion

In this problem, we calculated the average amount of corn produced per acre by dividing the total amount of corn produced by the total area of the farmland. We represented the answer in scientific notation as $$1.6 \times 10^2$$ bushels.

Key Takeaways

To find the average amount of corn produced per acre, we need to divide the total amount of corn produced by the total area of the farmland.
We can represent the answer in scientific notation as $$1.6 \times 10^2$$ bushels.

Practice Problems

A farmer has a total of $$5.4 \times 10^3$$ acres of farmland. Each year, the farm produces $$8.64 \times 10^5$$ bushels of wheat. What is the average amount of wheat produced per acre?
A rancher has a total of $$2.1 \times 10^2$$ acres of grazing land. Each year, the ranch produces $$3.24 \times 10^4$$ pounds of beef. What is the average amount of beef produced per acre?

Solutions

Average wheat production per acre = $$\frac{8.64 \times 10^5}{5.4 \times 10^3} = 1.6 \times 10^2$$ bushels
Average beef production per acre = $$\frac{3.24 \times 10^4}{2.1 \times 10^2} = 1.55 \times 10^2$$ pounds
Frequently Asked Questions (FAQs) about Calculating Average Corn Production per Acre =====================================================================================

Q: What is the formula for calculating average corn production per acre?

A: The formula for calculating average corn production per acre is:

Average corn production per acre = Total amount of corn produced / Total area of farmland

Q: How do I represent the answer in scientific notation?

A: To represent the answer in scientific notation, you need to divide the numerator and denominator by their greatest common factor, which is 10 raised to the power of the smallest exponent.

Q: What is the difference between average corn production per acre and total corn production?

A: The average corn production per acre is the amount of corn produced per acre, while the total corn production is the total amount of corn produced on the entire farm.

Q: How do I calculate the total area of the farmland?

A: The total area of the farmland is given in acres. You can represent it in scientific notation as 4.2 x 10^2 acres.

Q: How do I calculate the total amount of corn produced?

A: The total amount of corn produced is given in bushels. You can represent it in scientific notation as 6.72 x 10^4 bushels.

Q: What is the significance of calculating average corn production per acre?

A: Calculating average corn production per acre helps farmers and ranchers to determine the efficiency of their land use and make informed decisions about crop rotation, fertilization, and other agricultural practices.

Q: Can I use this formula to calculate average production for other crops?

A: Yes, you can use this formula to calculate average production for other crops, such as wheat, soybeans, and beef.

Q: What are some common mistakes to avoid when calculating average corn production per acre?

A: Some common mistakes to avoid when calculating average corn production per acre include:

Not converting the total area of the farmland to the same unit as the total amount of corn produced
Not simplifying the expression before evaluating it
Not representing the answer in scientific notation

Q: How can I apply this formula in real-world scenarios?

A: You can apply this formula in real-world scenarios by using it to calculate average production for different crops, determine the efficiency of land use, and make informed decisions about agricultural practices.

Q: What are some additional resources for learning more about calculating average corn production per acre?

A: Some additional resources for learning more about calculating average corn production per acre include:

Online tutorials and videos
Agricultural textbooks and manuals
Professional associations and organizations related to agriculture

Conclusion

Calculating average corn production per acre is an important concept in agriculture that helps farmers and ranchers to determine the efficiency of their land use and make informed decisions about crop rotation, fertilization, and other agricultural practices. By following the formula and avoiding common mistakes, you can accurately calculate average production for different crops and apply this knowledge in real-world scenarios.