Using the Weight of the Books

Oct 13, 2025 by miodeya.com 49 views

Introduction

In this article, we will delve into a problem involving the weights of two different versions of a book. The hardcover version of the book weighs 7 ounces, while its paperback version weighs 5 ounces. We are given that forty-five copies of the book weigh a total of 249 ounces. Our goal is to determine the number of hardcover and paperback copies.

The Problem

Let's break down the problem and understand what we are given. We have two types of books: hardcover and paperback. The hardcover version weighs 7 ounces, while the paperback version weighs 5 ounces. We are given that forty-five copies of the book weigh a total of 249 ounces. This can be represented by the following equation:

45x + 45y = 249

where x is the number of hardcover copies and y is the number of paperback copies.

The Equation

The equation 45x + 45y = 249 can be simplified by dividing both sides by 45:

x + y = 5.5

This equation represents the total number of copies of the book. Since we cannot have a fraction of a book, we can conclude that the total number of copies is 55.

Solving the Equation

Now that we have the total number of copies, we can substitute this value into the original equation:

45x + 45y = 249

We can also substitute x + y = 5.5 into the equation:

45(x + y) = 249

Expanding the equation, we get:

45x + 45y = 249

Substituting x + y = 5.5, we get:

45(5.5) = 249

Simplifying the equation, we get:

247.5 = 249

This equation is not true, which means that our assumption of x + y = 5.5 is incorrect. We need to find another way to solve the equation.

Using the Weight of the Books

Let's use the weight of the books to solve the equation. We know that the hardcover version weighs 7 ounces and the paperback version weighs 5 ounces. We can represent the weight of the books as:

Weight of hardcover books = 7x Weight of paperback books = 5y

The total weight of the books is 249 ounces, so we can set up the following equation:

7x + 5y = 249

We can also use the fact that x + y = 55 to substitute y = 55 - x into the equation:

7x + 5(55 - x) = 249

Expanding the equation, we get:

7x + 275 - 5x = 249

Simplifying the equation, we get:

2x = -26

Dividing both sides by 2, we get:

x = -13

This value of x is not possible, since we cannot have a negative number of books. We need to find another way to solve the equation.

Using the Ratio of the Weights

Let's use the ratio of the weights to solve the equation. We know that the hardcover version weighs 7 ounces and the paperback version weighs 5 ounces. We can represent the ratio of the weights as:

7:5

We can also represent the ratio of the number of books as:

x:y

Since the total number of books is 55, we can set up the following equation:

x + y = 55

We can also use the fact that the ratio of the weights is 7:5 to set up the following equation:

7x = 5y

We can substitute y = 55 - x into the equation:

7x = 5(55 - x)

Expanding the equation, we get:

7x = 275 - 5x

Simplifying the equation, we get:

12x = 275

Dividing both sides by 12, we get:

x = 22.9167

Since we cannot have a fraction of a book, we can round x to the nearest whole number:

x = 23

Substituting x = 23 into the equation x + y = 55, we get:

y = 32

Conclusion

In this article, we solved the problem of determining the number of hardcover and paperback copies of a book. We used the weight of the books and the ratio of the weights to solve the equation. We found that there are 23 hardcover copies and 32 paperback copies.

The Final Answer

The final answer is:

23 hardcover copies
32 paperback copies
The Weighty Problem of Book Weights: Q&A =====================================

Introduction

In our previous article, we solved the problem of determining the number of hardcover and paperback copies of a book. We used the weight of the books and the ratio of the weights to solve the equation. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the weight of a single hardcover book?

A: The weight of a single hardcover book is 7 ounces.

Q: What is the weight of a single paperback book?

A: The weight of a single paperback book is 5 ounces.

Q: How many copies of the book weigh a total of 249 ounces?

A: Forty-five copies of the book weigh a total of 249 ounces.

Q: How did you solve the equation 45x + 45y = 249?

A: We solved the equation by using the weight of the books and the ratio of the weights. We first simplified the equation by dividing both sides by 45, which gave us x + y = 5.5. However, this equation is not true, so we had to find another way to solve the equation. We used the fact that the ratio of the weights is 7:5 to set up the equation 7x = 5y. We then substituted y = 55 - x into the equation and solved for x.

Q: What is the ratio of the weights of the hardcover and paperback books?

A: The ratio of the weights of the hardcover and paperback books is 7:5.

Q: How did you find the number of hardcover and paperback copies?

A: We found the number of hardcover and paperback copies by using the ratio of the weights. We set up the equation 7x = 5y and substituted y = 55 - x into the equation. We then solved for x and found that x = 23. We then substituted x = 23 into the equation x + y = 55 and found that y = 32.

Q: What is the total number of copies of the book?

A: The total number of copies of the book is 55.

Q: Can you explain the solution in more detail?

A: Yes, we can explain the solution in more detail. We first simplified the equation 45x + 45y = 249 by dividing both sides by 45, which gave us x + y = 5.5. However, this equation is not true, so we had to find another way to solve the equation. We used the fact that the ratio of the weights is 7:5 to set up the equation 7x = 5y. We then substituted y = 55 - x into the equation and solved for x. We found that x = 23 and then substituted x = 23 into the equation x + y = 55 to find that y = 32.

Conclusion

In this article, we answered some frequently asked questions related to the problem of determining the number of hardcover and paperback copies of a book. We used the weight of the books and the ratio of the weights to solve the equation and found that there are 23 hardcover copies and 32 paperback copies.

The Final Answer

The final answer is:

23 hardcover copies
32 paperback copies