Teachers' Editions Of A Statistics Textbook Sell For $\$150$ Each, And Students' Editions Of The Book Sell For $\$50$ Each. Which Function Can Be Used To Find The Average Cost Per Book If Two Teachers' Editions And $x$

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Introduction

In the world of mathematics, understanding the cost of textbooks is crucial for both teachers and students. The cost of textbooks can vary greatly depending on the edition and the purpose of the book. In this article, we will explore the cost of teachers' and students' editions of a statistics textbook and determine which function can be used to find the average cost per book.

The Cost of Teachers' and Students' Editions

The cost of teachers' editions of a statistics textbook is $150\$150 each, while the cost of students' editions is $50\$50 each. If two teachers' editions and xx students' editions are purchased, the total cost can be calculated as follows:

  • The cost of two teachers' editions is 2×$150=$3002 \times \$150 = \$300.
  • The cost of xx students' editions is x×$50=$50xx \times \$50 = \$50x.

Calculating the Total Cost

The total cost of purchasing two teachers' editions and xx students' editions can be calculated by adding the cost of the teachers' editions and the cost of the students' editions:

Total Cost=$300+$50x\text{Total Cost} = \$300 + \$50x

Determining the Average Cost per Book

To find the average cost per book, we need to divide the total cost by the total number of books purchased. Since two teachers' editions and xx students' editions are purchased, the total number of books is 2+x2 + x. Therefore, the average cost per book can be calculated as follows:

Average Cost per Book=$300+$50x2+x\text{Average Cost per Book} = \frac{\$300 + \$50x}{2 + x}

Simplifying the Function

The function for the average cost per book can be simplified by factoring out the common term $50\$50 from the numerator:

Average Cost per Book=$300+$50x2+x=$50(6+x)2+x=$50×6+x2+x\text{Average Cost per Book} = \frac{\$300 + \$50x}{2 + x} = \frac{\$50(6 + x)}{2 + x} = \$50 \times \frac{6 + x}{2 + x}

Understanding the Function

The function for the average cost per book is a rational function, which is a function that can be expressed as the ratio of two polynomials. In this case, the function is:

Average Cost per Book=$50×6+x2+x\text{Average Cost per Book} = \$50 \times \frac{6 + x}{2 + x}

This function represents the average cost per book as a function of the number of students' editions purchased, xx. The function has a constant term of $50\$50 and a variable term of $50x\$50x, which represents the cost of the students' editions.

Graphing the Function

The graph of the function can be used to visualize the relationship between the average cost per book and the number of students' editions purchased. The graph will have a horizontal asymptote at $150\$150, which represents the cost of a teachers' edition. The graph will also have a vertical asymptote at x=−2x = -2, which represents the point at which the number of students' editions purchased is negative.

Conclusion

In conclusion, the function for the average cost per book is $50×6+x2+x\$50 \times \frac{6 + x}{2 + x}. This function represents the average cost per book as a function of the number of students' editions purchased, xx. The function has a constant term of $50\$50 and a variable term of $50x\$50x, which represents the cost of the students' editions. The graph of the function can be used to visualize the relationship between the average cost per book and the number of students' editions purchased.

References

Appendix

The following is a list of the variables used in the function:

  • xx: The number of students' editions purchased.
  • $50\$50: The cost of a students' edition.
  • $150\$150: The cost of a teachers' edition.
  • $300\$300: The cost of two teachers' editions.
  • $50x\$50x: The cost of xx students' editions.
  • $300+$50x\$300 + \$50x: The total cost of purchasing two teachers' editions and xx students' editions.
  • $300+$50x2+x\frac{\$300 + \$50x}{2 + x}: The function for the average cost per book.
  • $50×6+x2+x\$50 \times \frac{6 + x}{2 + x}: The simplified function for the average cost per book.
    Frequently Asked Questions: Understanding the Cost of Statistics Textbooks ====================================================================

Q: What is the cost of a teachers' edition of a statistics textbook?

A: The cost of a teachers' edition of a statistics textbook is $150\$150.

Q: What is the cost of a students' edition of a statistics textbook?

A: The cost of a students' edition of a statistics textbook is $50\$50.

Q: If two teachers' editions and xx students' editions are purchased, what is the total cost?

A: The total cost can be calculated as follows:

Total Cost=$300+$50x\text{Total Cost} = \$300 + \$50x

Q: How can I find the average cost per book if two teachers' editions and xx students' editions are purchased?

A: To find the average cost per book, you can use the following function:

Average Cost per Book=$300+$50x2+x\text{Average Cost per Book} = \frac{\$300 + \$50x}{2 + x}

Q: Can I simplify the function for the average cost per book?

A: Yes, the function can be simplified by factoring out the common term $50\$50 from the numerator:

Average Cost per Book=$300+$50x2+x=$50(6+x)2+x=$50×6+x2+x\text{Average Cost per Book} = \frac{\$300 + \$50x}{2 + x} = \frac{\$50(6 + x)}{2 + x} = \$50 \times \frac{6 + x}{2 + x}

Q: What is the horizontal asymptote of the graph of the function for the average cost per book?

A: The horizontal asymptote of the graph of the function for the average cost per book is $150\$150, which represents the cost of a teachers' edition.

Q: What is the vertical asymptote of the graph of the function for the average cost per book?

A: The vertical asymptote of the graph of the function for the average cost per book is x=−2x = -2, which represents the point at which the number of students' editions purchased is negative.

Q: Can I use the function for the average cost per book to determine the cost of purchasing a certain number of students' editions?

A: Yes, you can use the function to determine the cost of purchasing a certain number of students' editions by plugging in the value of xx into the function.

Q: What is the relationship between the average cost per book and the number of students' editions purchased?

A: The average cost per book is directly proportional to the number of students' editions purchased. As the number of students' editions increases, the average cost per book also increases.

Q: Can I use the function for the average cost per book to compare the cost of purchasing different numbers of students' editions?

A: Yes, you can use the function to compare the cost of purchasing different numbers of students' editions by plugging in different values of xx into the function.

Q: What is the significance of the function for the average cost per book in real-world applications?

A: The function for the average cost per book is significant in real-world applications because it can be used to determine the cost of purchasing a certain number of students' editions, which is an important consideration for educators and administrators.

Q: Can I use the function for the average cost per book to make predictions about the cost of purchasing students' editions in the future?

A: Yes, you can use the function to make predictions about the cost of purchasing students' editions in the future by plugging in future values of xx into the function.

Q: What are some potential limitations of the function for the average cost per book?

A: Some potential limitations of the function for the average cost per book include:

  • The function assumes that the cost of a teachers' edition is $150\$150 and the cost of a students' edition is $50\$50.
  • The function does not take into account any potential discounts or promotions that may be available.
  • The function assumes that the number of students' editions purchased is a continuous variable, when in reality it may be a discrete variable.

Q: Can I use the function for the average cost per book to make decisions about purchasing students' editions?

A: Yes, you can use the function to make decisions about purchasing students' editions by considering the average cost per book and the number of students' editions that need to be purchased. However, it is also important to consider other factors, such as the quality of the textbook and the availability of other resources.