Select The Correct Answer.A Drugstore Sells Vitamins In Bottles With Different Pill Counts. The Price Of Each Bottle Is Shown In The Table Below.$[ \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Number Of \ Pills \end{tabular} & Price

by ADMIN 237 views

Introduction

In this article, we will delve into a real-world problem involving the pricing of vitamins in a drugstore. The problem is presented in a table showing the number of pills in each bottle and their corresponding prices. Our task is to analyze the given data and determine the correct answer to the problem.

Problem Statement

A drugstore sells vitamins in bottles with different pill counts. The price of each bottle is shown in the table below.

Number of Pills Price
10 $0.50
20 $1.00
30 $1.50
40 $2.00
50 $2.50
60 $3.00
70 $3.50
80 $4.00
90 $4.50
100 $5.00

Analysis

To solve this problem, we need to examine the given data and look for any patterns or relationships between the number of pills and the price. Upon closer inspection, we notice that the price of each bottle increases by $0.50 for every 10 pills.

Number of Pills Price Increase
10 $0.50 -
20 $1.00 $0.50
30 $1.50 $0.50
40 $2.00 $0.50
50 $2.50 $0.50
60 $3.00 $0.50
70 $3.50 $0.50
80 $4.00 $0.50
90 $4.50 $0.50
100 $5.00 $0.50

As we can see, the price increases by $0.50 for every 10 pills, which suggests a linear relationship between the number of pills and the price.

Conclusion

Based on our analysis, we can conclude that the correct answer to the problem is that the price of each bottle increases by $0.50 for every 10 pills.

Mathematical Representation

We can represent the relationship between the number of pills and the price using a linear equation. Let x be the number of pills and y be the price. Then, we can write the equation as:

y = 0.05x + b

where b is the y-intercept.

To find the value of b, we can use the given data points. For example, when x = 10, y = 0.50. Substituting these values into the equation, we get:

0.50 = 0.05(10) + b 0.50 = 0.5 + b b = 0

Therefore, the linear equation representing the relationship between the number of pills and the price is:

y = 0.05x

Discussion

This problem is a classic example of a linear relationship between two variables. The price of each bottle increases by $0.50 for every 10 pills, which is a clear indication of a linear relationship.

In real-world applications, linear relationships are common in many fields, including economics, physics, and engineering. Understanding linear relationships is essential in making predictions, modeling real-world phenomena, and making informed decisions.

Real-World Applications

The concept of linear relationships has numerous real-world applications. For example:

  • In economics, linear relationships are used to model the demand and supply of goods and services.
  • In physics, linear relationships are used to describe the motion of objects under the influence of gravity or other forces.
  • In engineering, linear relationships are used to design and optimize systems, such as electrical circuits and mechanical systems.

Conclusion

In conclusion, the problem presented in this article is a classic example of a linear relationship between two variables. The price of each bottle increases by $0.50 for every 10 pills, which is a clear indication of a linear relationship. Understanding linear relationships is essential in making predictions, modeling real-world phenomena, and making informed decisions.

References

Appendix

The following table shows the number of pills and the corresponding price for each bottle.

Number of Pills Price
10 $0.50
20 $1.00
30 $1.50
40 $2.00
50 $2.50
60 $3.00
70 $3.50
80 $4.00
90 $4.50
100 $5.00

Introduction

In our previous article, we delved into a real-world problem involving the pricing of vitamins in a drugstore. The problem is presented in a table showing the number of pills in each bottle and their corresponding prices. Our task is to analyze the given data and determine the correct answer to the problem.

Q&A

Q: What is the relationship between the number of pills and the price?

A: The price of each bottle increases by $0.50 for every 10 pills, which is a clear indication of a linear relationship.

Q: How can we represent the relationship between the number of pills and the price using a linear equation?

A: We can represent the relationship using the equation y = 0.05x, where x is the number of pills and y is the price.

Q: What is the y-intercept of the linear equation?

A: The y-intercept is 0, which means that when the number of pills is 0, the price is also 0.

Q: What are some real-world applications of linear relationships?

A: Linear relationships are used in many fields, including economics, physics, and engineering. For example, in economics, linear relationships are used to model the demand and supply of goods and services. In physics, linear relationships are used to describe the motion of objects under the influence of gravity or other forces. In engineering, linear relationships are used to design and optimize systems, such as electrical circuits and mechanical systems.

Q: How can we use the concept of linear relationships to make predictions or model real-world phenomena?

A: By understanding the linear relationship between two variables, we can make predictions about the behavior of the system or model the real-world phenomenon. For example, if we know the price of a bottle of vitamins and the number of pills it contains, we can use the linear equation to predict the price of a bottle with a different number of pills.

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

A: Some common mistakes to avoid when working with linear relationships include:

  • Assuming a linear relationship when it is not present
  • Failing to account for non-linear effects or interactions between variables
  • Using a linear equation to model a non-linear relationship
  • Failing to consider the limitations and assumptions of the linear equation

Q: How can we determine if a linear relationship is present in a set of data?

A: We can determine if a linear relationship is present in a set of data by plotting the data points on a graph and examining the resulting pattern. If the data points form a straight line, then a linear relationship is likely present.

Q: What are some tools or techniques that can be used to analyze and visualize linear relationships?

A: Some tools or techniques that can be used to analyze and visualize linear relationships include:

  • Graphing calculators or software
  • Statistical analysis software
  • Data visualization tools
  • Linear regression analysis

Conclusion

In conclusion, the vitamins pricing problem is a classic example of a linear relationship between two variables. By understanding the linear relationship between the number of pills and the price, we can make predictions, model real-world phenomena, and make informed decisions. We hope that this Q&A article has provided a helpful resource for those looking to learn more about linear relationships and how to apply them in real-world situations.

References

Appendix

The following table shows the number of pills and the corresponding price for each bottle.

Number of Pills Price
10 $0.50
20 $1.00
30 $1.50
40 $2.00
50 $2.50
60 $3.00
70 $3.50
80 $4.00
90 $4.50
100 $5.00