# A country produces books and video games exclusively. In the same time it takes to produce one video game, the country could produce 4 books. If the country currently produces 800 books and 200 video games but would like to consume a combination of 100 video games and 1,400 books, which of the following is true?

a. The country can produce 600 more books and 100 fewer video games itself, or it can engage in trade.
b. The country might consume 100 video games and 1,400 books following trade.
c. This is only possible if the country produces 600 more books and 100 fewer video games itself.
d. It is impossible for the country to consume a combination of 100 video games and 1,400 books.

## To solve this problem, let's analyze the production and consumption of books and video games.

Given that, in the same time it takes to produce one video game, the country could produce 4 books.

Currently, the country produces 800 books and 200 video games. Therefore, it takes 3 books to produce one video game (800 books / 200 video games = 4 books per video game).

We want to consume a combination of 100 video games and 1,400 books.

To produce 100 video games, it would take 300 books (100 video games * 3 books per video game = 300 books).
To produce 1,400 books, it would take 350 video games (1,400 books / 4 books per video game = 350 video games).

So, in order for the country to consume a combination of 100 video games and 1,400 books:
- The country needs to produce 300 books (to use for video game production) instead of the current 800 books (-500 books).
- The country needs to produce 450 video games (to use for book production) instead of the current 200 video games (+250 video games).

Therefore, the correct answer is:

a. The country can produce 600 more books and 100 fewer video games itself, or it can engage in trade.

## To determine which of the statements is true, we need to analyze the production possibilities and the desired consumption.

Given:
- The country produces books and video games exclusively.
- It takes the same time to produce one video game as it does to produce four books.
- The country currently produces 800 books and 200 video games.

Now, let's calculate the production capacity of the country:

If it takes the same time to produce one video game as it does to produce four books, and currently, the country produces 800 books, we can determine the number of video games produced:

800 books * (1 video game / 4 books) = 200 video games

So, the current production capacity of the country is 800 books and 200 video games.

Next, let's determine the desired consumption:

The country wants to consume a combination of 100 video games and 1,400 books.

Now, we need to compare the production capacity and the desired consumption:

Compare the desired consumption to the current production capacity:
- Desired books: 1,400 books
- Available books: 800 books

Since the available books (800) are less than the desired books (1,400), the country needs to acquire more books.

Now, calculate the deficit in books:

Deficit in books = Desired books - Available books
Deficit in books = 1,400 books - 800 books
Deficit in books = 600 books

Now, let's compare the video games:

Compare the desired consumption to the current production capacity:
- Desired video games: 100 video games
- Available video games: 200 video games

Since the available video games (200) are more than the desired video games (100), the country has an excess of video games.

Now, calculate the excess in video games:

Excess in video games = Available video games - Desired video games
Excess in video games = 200 video games - 100 video games
Excess in video games = 100 video games

Based on the analysis, it is clear that statement a. "The country can produce 600 more books and 100 fewer video games itself, or it can engage in trade" is true. The country can increase its book production by 600 and reduce its video game production by 100 to satisfy its desired consumption.

Therefore, the correct answer is a. The country can produce 600 more books and 100 fewer video games itself, or it can engage in trade.