The Recipe For Beef Stew Calls For $\frac{1}{4}$ Teaspoon Of Pepper For Every 3 Potatoes. If 9 Potatoes Are Used, How Much Pepper Is Needed?Which Proportion Represents This Problem?A. $\frac{1/4}{3} = \frac{9}{p}$B. $\frac{1/4}{3}

The Recipe for Beef Stew: A Proportion Problem

Understanding the Problem

When it comes to cooking, proportions are essential to ensure that the dish turns out right. In this case, we have a recipe for beef stew that calls for a specific amount of pepper for every 3 potatoes. The question is, if 9 potatoes are used, how much pepper is needed? To solve this problem, we need to set up a proportion that represents the given information.

Setting Up the Proportion

The proportion that represents this problem is:

$\frac{1/4}{3} = \frac{9}{p}$

Where $p$ is the amount of pepper needed for 9 potatoes.

Breaking Down the Proportion

Let's break down the proportion and understand what each part represents:

• $\frac{1/4}{3}$: This is the ratio of pepper to potatoes in the original recipe. It means that for every 3 potatoes, 1/4 teaspoon of pepper is needed.
• $\frac{9}{p}$: This is the ratio of potatoes to pepper that we want to find. We know that 9 potatoes are used, and we want to find out how much pepper is needed.

Solving the Proportion

To solve the proportion, we can cross-multiply:

$\frac{1/4}{3} = \frac{9}{p}$

$1/4 \cdot p = 9 \cdot 3$

$p = \frac{9 \cdot 3}{1/4}$

$p = \frac{27}{1/4}$

$p = 27 \cdot 4$

$p = 108$

Conclusion

Therefore, if 9 potatoes are used in the recipe for beef stew, 108 times the amount of pepper called for in the original recipe is needed.

Why This Problem Matters

This problem may seem simple, but it's a great example of how proportions can be used in real-life situations. In cooking, proportions are essential to ensure that the dish turns out right. This problem also demonstrates the importance of understanding ratios and proportions in mathematics.

Real-World Applications

Proportions are used in many real-world applications, including:

• Cooking and baking
• Science and engineering
• Finance and economics
• Architecture and design

Tips and Tricks

When working with proportions, it's essential to:

• Read the problem carefully and understand what's being asked
• Set up the proportion correctly
• Solve the proportion using cross-multiplication
• Check your answer to make sure it makes sense in the context of the problem

Common Mistakes

When working with proportions, common mistakes include:

• Not reading the problem carefully
• Setting up the proportion incorrectly
• Not solving the proportion using cross-multiplication
• Not checking the answer to make sure it makes sense in the context of the problem

Conclusion

In conclusion, the recipe for beef stew calls for $\frac{1}{4}$ teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed? The proportion that represents this problem is $\frac{1/4}{3} = \frac{9}{p}$. By solving the proportion, we find that 108 times the amount of pepper called for in the original recipe is needed. This problem demonstrates the importance of understanding ratios and proportions in mathematics and highlights the real-world applications of proportions.
The Recipe for Beef Stew: A Proportion Problem - Q&A

Understanding the Problem

In our previous article, we explored the recipe for beef stew and how to set up a proportion to find the amount of pepper needed for 9 potatoes. In this article, we'll answer some common questions related to the problem.

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It's a way of expressing a relationship between two quantities. In the case of the beef stew recipe, the proportion is $\frac{1/4}{3} = \frac{9}{p}$, where $p$ is the amount of pepper needed for 9 potatoes.

Q: Why do we need to set up a proportion?

A: We need to set up a proportion because it allows us to find the unknown quantity (in this case, the amount of pepper needed for 9 potatoes) by using the known quantities (the ratio of pepper to potatoes in the original recipe).

Q: How do I know which quantities to use in the proportion?

A: To set up a proportion, you need to identify the known and unknown quantities. In this case, the known quantity is the ratio of pepper to potatoes in the original recipe ($\frac{1/4}{3}$), and the unknown quantity is the amount of pepper needed for 9 potatoes ($p$).

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to solve proportions. It involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. In the case of the beef stew recipe, we cross-multiply as follows:

$\frac{1/4}{3} = \frac{9}{p}$

$1/4 \cdot p = 9 \cdot 3$

Q: Why do we need to check our answer?

A: We need to check our answer to make sure it makes sense in the context of the problem. In this case, we need to check that the amount of pepper needed for 9 potatoes is a reasonable quantity.

Q: What are some common mistakes to avoid when working with proportions?

A: Some common mistakes to avoid when working with proportions include:

• Not reading the problem carefully
• Setting up the proportion incorrectly
• Not solving the proportion using cross-multiplication
• Not checking the answer to make sure it makes sense in the context of the problem

Q: How can I apply proportions to real-world problems?

A: Proportions can be applied to a wide range of real-world problems, including:

• Cooking and baking
• Science and engineering
• Finance and economics
• Architecture and design

Q: What are some tips for solving proportions?

A: Some tips for solving proportions include:

• Read the problem carefully and understand what's being asked
• Set up the proportion correctly
• Solve the proportion using cross-multiplication
• Check your answer to make sure it makes sense in the context of the problem

Conclusion

In conclusion, the recipe for beef stew calls for $\frac{1}{4}$ teaspoon of pepper for every 3 potatoes. If 9 potatoes are used, how much pepper is needed? By setting up a proportion and solving it using cross-multiplication, we find that 108 times the amount of pepper called for in the original recipe is needed. This problem demonstrates the importance of understanding ratios and proportions in mathematics and highlights the real-world applications of proportions.