A Grocer Sells Oranges In Bags. Each Empty Bag Weighs A Certain Amount. If A Bag Of Oranges Weighs 60.1 Ounces, Which Equation Represents The Total Weight?A. 7.2 + X = 60.1 7.2 + X = 60.1 7.2 + X = 60.1 B. 2.5 X + 7.2 = 60.1 2.5x + 7.2 = 60.1 2.5 X + 7.2 = 60.1 C. 60.1 − X = 2.5 + 7.2 60.1 - X = 2.5 + 7.2 60.1 − X = 2.5 + 7.2 D.

As a grocer, selling oranges in bags can be a profitable venture. However, it's essential to consider the weight of the empty bags, as it can significantly impact the overall weight of the oranges. In this scenario, we're given that a bag of oranges weighs 60.1 ounces, and we need to determine the equation that represents the total weight. Let's dive into the problem and explore the possible solutions.

Understanding the Problem

The problem states that a bag of oranges weighs 60.1 ounces. We're also told that the empty bag weighs a certain amount, which we'll denote as x. Our goal is to find the equation that represents the total weight of the oranges and the empty bag.

Analyzing the Options

Let's examine each of the given options and determine which one represents the total weight of the oranges and the empty bag.

Option A: $7.2 + x = 60.1$

This equation suggests that the total weight is the sum of the weight of the empty bag (x) and a constant value of 7.2. However, this doesn't seem to accurately represent the situation, as the weight of the empty bag is not explicitly mentioned.

Option B: $2.5x + 7.2 = 60.1$

This equation implies that the total weight is the product of the weight of the empty bag (x) and a constant factor of 2.5, plus a constant value of 7.2. This option seems more plausible, as it takes into account the weight of the empty bag and a possible factor that affects its weight.

Option C: $60.1 - x = 2.5 + 7.2$

This equation suggests that the total weight is the difference between the weight of the oranges (60.1) and the weight of the empty bag (x). However, this option doesn't seem to accurately represent the situation, as it doesn't take into account the possible factor that affects the weight of the empty bag.

Option D: (No equation provided)

This option is not a valid equation, as it doesn't provide a mathematical representation of the total weight.

Conclusion

Based on our analysis, the most plausible equation that represents the total weight of the oranges and the empty bag is:

$2.5x + 7.2 = 60.1$

This equation takes into account the weight of the empty bag (x) and a possible factor that affects its weight, as well as a constant value of 7.2. By solving this equation, we can determine the weight of the empty bag and the total weight of the oranges and the empty bag.

Solving the Equation

To solve the equation $2.5x + 7.2 = 60.1$, we can use algebraic manipulation to isolate the variable x.

First, we'll subtract 7.2 from both sides of the equation:

$2.5x = 60.1 - 7.2$

$2.5x = 52.9$

Next, we'll divide both sides of the equation by 2.5 to solve for x:

$x = \frac{52.9}{2.5}$

$x = 21.16$

Therefore, the weight of the empty bag is approximately 21.16 ounces.

Total Weight

Now that we've determined the weight of the empty bag, we can calculate the total weight of the oranges and the empty bag by substituting the value of x into the equation:

$2.5x + 7.2 = 2.5(21.16) + 7.2$

$2.5(21.16) + 7.2 = 52.9 + 7.2$

$52.9 + 7.2 = 60.1$

As expected, the total weight of the oranges and the empty bag is 60.1 ounces.

Conclusion

$$

Q&A: Understanding the Weighty Problem of Oranges in Bags

In our previous article, we explored the problem of a grocer selling oranges in bags and determined the equation that represents the total weight. However, we understand that some readers may still have questions about the problem. In this article, we'll address some of the most frequently asked questions and provide additional insights into the problem.

Q: What is the weight of the empty bag?

A: The weight of the empty bag is approximately 21.16 ounces, as determined by solving the equation $2.5x + 7.2 = 60.1$.

Q: How did you determine the weight of the empty bag?

A: We determined the weight of the empty bag by solving the equation $2.5x + 7.2 = 60.1$. We first subtracted 7.2 from both sides of the equation to isolate the term with the variable x. Then, we divided both sides of the equation by 2.5 to solve for x.

Q: What is the total weight of the oranges and the empty bag?

A: The total weight of the oranges and the empty bag is 60.1 ounces, as determined by substituting the value of x into the equation $2.5x + 7.2 = 60.1$.

Q: Why is it important to consider the weight of the empty bags?

A: It's essential to consider the weight of the empty bags when selling oranges in bags because it can significantly impact the overall weight of the oranges. If the weight of the empty bags is not taken into account, the grocer may end up selling oranges that are heavier than expected, which can lead to customer dissatisfaction and financial losses.

Q: How can I apply this problem to real-life situations?

A: This problem can be applied to real-life situations where you need to consider the weight of empty containers or packaging materials. For example, if you're a manufacturer of food products, you may need to consider the weight of empty packaging materials when calculating the total weight of the product. By using algebraic manipulation, you can determine the weight of the empty containers and the total weight of the product.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include:

• Not considering the weight of the empty bags
• Not using algebraic manipulation to solve for the variable x
• Not substituting the value of x into the equation to determine the total weight
• Not taking into account the possible factor that affects the weight of the empty bags

Conclusion

In conclusion, the problem of a grocer selling oranges in bags is a classic example of how algebraic manipulation can be used to solve equations and determine unknown values. By understanding the weighty problem of oranges in bags, you can apply this problem to real-life situations and avoid common mistakes. We hope this Q&A article has provided additional insights into the problem and has helped you better understand the importance of considering the weight of empty bags.