Question

Last week, Russell bought 8 books and 4 movies for a total of $76. Today, Russell bought 5 books and 7 movies for a total of $97 . Assuming neither item has changed in price , what is the cost of a book in dollars ?

Answer 1

To find the cost of a book, we set up two equations from the given transactions and solved the system of equations. After solving, we found that each book costs $4.

Step-by-step explanation:

To determine the cost of a book, we need to set up a system of equations based on the information provided. Let b represent the cost of a book and m represent the cost of a movie. We are given two transactions:

• 8 books and 4 movies for a total of $76
• 5 books and 7 movies for a total of $97

These transactions can be represented by two equations:

1. 8b + 4m = 76
2. 5b + 7m = 97

Solving this system of equations will give us the individual prices of books and movies. We can start by multiplying the first equation by 7 and the second equation by 4 to eliminate the m variable:

1. 56b + 28m = 532
2. 20b + 28m = 388

Subtracting the second equation from the first gives us:

1. 36b = 144

Dividing both sides by 36, we find that b (the price of a book) is $4. Therefore, each book costs $4.