F. Suppose Santiago bought 26 books. Can you figure out how many of each type of book he bought? Explain. Write a system of equations and solve algebraically. Use Demos Calculator to check your work by adding the equation x + y = 26 to the graph above to help you answer the question

Answer 1

To determine how many of each type of book Santiago bought, we can set up a system of equations. Let’s assume the following variables:

• Let \( x \) represent the number of fiction books.
• Let \( y \) represent the number of non-fiction books.

From the problem, we have the following information:

1. The total number of books bought by Santiago is 26: \[ x + y = 26 \]

To solve this system, we need another equation, which depends on additional information about the relationship between fiction and non-fiction books (e.g., perhaps he bought twice as many fiction books as non-fiction books). Let’s assume the second equation is: \[ x = 2y \]

Now, we have the following system of equations:

1. \( x + y = 26 \)
2. \( x = 2y \)

Step 1: Substitute the second equation into the first

Substituting \( x = 2y \) into \( x + y = 26 \): \[ 2y + y = 26 \] \[ 3y = 26 \] \[ y = \frac{26}{3} \approx 8.67 \]

Step 2: Solve for \( x \)

Now, substituting \( y \) back into \( x = 2y \): \[ x = 2 \times \frac{26}{3} = \frac{52}{3} \approx 17.33 \]

Conclusion

Thus, Santiago bought approximately \( 17.33 \) fiction books and \( 8.67 \) non-fiction books, which doesn't make logical sense since he can't buy a fraction of a book.

Correct Approach:

Since we reached an impractical solution, let’s analyze this systematically. The problem may not provide enough constraints.

Revisit Equations

To create proper integer solutions, we need clear relationships between types of books.

Assuming:

• \( x = \) number of fiction books
• \( y = \) number of non-fiction books

Have the equations:

1. \( x + y = 26 \)
2. Suppose \( y = x - 2 \) (for some relationship)

Substituting \( y = 26 - x \):

We can also try integer pairs:

• If \( y = x - n\) for integers where \( n = 0, 1,…\) up to a point until their sum makes 26.

Solve using integers:

Trying pairs:

• \( y=10 \) leads \( x=16 \) corresponding to viable integer solutions.

You can adjust until you find \( x, y \) integers strictly adhering to relationships (if any given).

Checking the Solution

Using Demos Calculator can provide all pairs satisfying \( x + y = 26 \) and validate through graphing.

Final Notes: Provide constraints or relationships for better-defined solutions!