A Farmer Has Enough Food To Feed 35 Cows In His Shed For 9 Days. How Long Would The Food Last, If He Buys 10 More Cows?
Understanding the Problem
Mathematical problems like this one often require us to think critically and apply our knowledge of ratios and proportions. In this case, we are given that a farmer has enough food to feed 35 cows for 9 days. We need to determine how long the food would last if the farmer buys 10 more cows.
Initial Situation
The farmer has enough food to feed 35 cows for 9 days. This means that the total amount of food available is sufficient for 35 cows for 9 days. We can represent this situation using a ratio:
- 35 cows : 9 days
Adding More Cows
If the farmer buys 10 more cows, the total number of cows will become 35 + 10 = 45 cows. We need to find out how long the food will last for 45 cows.
Setting Up a Proportion
To solve this problem, we can set up a proportion using the initial situation and the new situation with 45 cows. The proportion can be written as:
- 35 cows : 9 days = 45 cows : x days
Solving the Proportion
To solve the proportion, we can cross-multiply and then divide both sides by the number of cows:
- 35x = 45 * 9
- 35x = 405
- x = 405 / 35
- x = 11.57 days
Conclusion
Therefore, if the farmer buys 10 more cows, the food will last for approximately 11.57 days.
Real-World Applications
This type of problem has real-world applications in various fields, such as:
- Agriculture: Farmers need to plan and manage their resources, including food for their livestock.
- Business: Companies need to estimate and manage their inventory, including food and other supplies.
- Science: Scientists need to understand and apply mathematical concepts to solve problems in various fields, including biology and ecology.
Tips and Tricks
- Ratios and proportions: Understanding ratios and proportions is crucial in solving problems like this one.
- Cross-multiplication: Cross-multiplication is a useful technique for solving proportions.
- Estimation: Estimating the answer is essential in problems like this one, where the exact answer may not be necessary.
Practice Problems
- A farmer has enough food to feed 20 chickens for 12 days. How long would the food last if the farmer buys 5 more chickens?
- A company has enough supplies to last for 15 days. If the company orders 20 more boxes of supplies, how long will the supplies last?
Solutions
- A farmer has enough food to feed 20 chickens for 12 days. If the farmer buys 5 more chickens, the food will last for approximately 10.71 days.
- A company has enough supplies to last for 15 days. If the company orders 20 more boxes of supplies, the supplies will last for approximately 14.29 days.
Conclusion
In conclusion, this problem requires us to apply our knowledge of ratios and proportions to solve a real-world problem. By setting up a proportion and solving it, we can determine how long the food will last if the farmer buys 10 more cows. This type of problem has real-world applications in various fields, and understanding ratios and proportions is essential in solving problems like this one.
Q&A Section
Q: What is the initial situation in this problem?
A: The farmer has enough food to feed 35 cows for 9 days.
Q: How many cows will the farmer have if he buys 10 more cows?
A: The farmer will have 35 + 10 = 45 cows.
Q: What is the proportion that we need to set up to solve this problem?
A: The proportion is 35 cows : 9 days = 45 cows : x days.
Q: How do we solve the proportion?
A: We can cross-multiply and then divide both sides by the number of cows.
Q: What is the solution to the proportion?
A: x = 405 / 35 = 11.57 days.
Q: What is the real-world application of this problem?
A: This type of problem has real-world applications in various fields, such as agriculture, business, and science.
Q: What are some tips and tricks for solving problems like this one?
A: Understanding ratios and proportions, cross-multiplication, and estimation are all essential skills for solving problems like this one.
Q: Can you provide some practice problems for readers to try?
A: Yes, here are a few practice problems:
- A farmer has enough food to feed 20 chickens for 12 days. How long would the food last if the farmer buys 5 more chickens?
- A company has enough supplies to last for 15 days. If the company orders 20 more boxes of supplies, how long will the supplies last?
Q: Can you provide the solutions to the practice problems?
A: Yes, here are the solutions:
- A farmer has enough food to feed 20 chickens for 12 days. If the farmer buys 5 more chickens, the food will last for approximately 10.71 days.
- A company has enough supplies to last for 15 days. If the company orders 20 more boxes of supplies, the supplies will last for approximately 14.29 days.
Q: What is the conclusion of this problem?
A: In conclusion, this problem requires us to apply our knowledge of ratios and proportions to solve a real-world problem. By setting up a proportion and solving it, we can determine how long the food will last if the farmer buys 10 more cows.
Frequently Asked Questions
Q: What is the formula for solving proportions?
A: The formula for solving proportions is:
a/b = c/d
where a, b, c, and d are the values in the proportion.
Q: How do I cross-multiply in a proportion?
A: To cross-multiply in a proportion, you multiply the numerator of the first fraction by the denominator of the second fraction, and then multiply the numerator of the second fraction by the denominator of the first fraction.
Q: What is the difference between a ratio and a proportion?
A: A ratio is a comparison of two or more numbers, while a proportion is a statement that two ratios are equal.
Additional Resources
- For more information on ratios and proportions, check out the following resources:
- Khan Academy: Ratios and Proportions
- Mathway: Ratios and Proportions
- Wolfram Alpha: Ratios and Proportions
- For more practice problems and solutions, check out the following resources:
- IXL: Ratios and Proportions
- Math Open Reference: Ratios and Proportions
- Purplemath: Ratios and Proportions