Santiago is working at his mom’s day care this summer. His mom has asked him to check out the library book sale to look for books they might be able to use in the day care. When he gets to the book sale, he sees that board books are $1.50 and soft cover books are $0.50. He picks out a variety of books and spends $20.

Let \( x \) be the number of board books Santiago buys, and \( y \) be the number of soft cover books Santiago buys.

The cost for board books is $1.50 each, so the total cost for board books is \( 1.50x \).

The cost for soft cover books is $0.50 each, so the total cost for soft cover books is \( 0.50y \).

Santiago spends a total of $20 on both types of books, which can be expressed with the following equation:

\[ 1.50x + 0.50y = 20 \]

This equation represents the relationship between the number of board books and soft cover books that Santiago buys and the total amount spent.

Is it possible that Santiago bought 10 board books and five soft cover books? Use your
equation from part A to check. Explain your answer.

To determine if Santiago could have bought 10 board books and 5 soft cover books, we can substitute \( x = 10 \) and \( y = 5 \) into the equation:

\[ 1.50x + 0.50y = 20 \]

Substituting in the values:

\[ 1.50(10) + 0.50(5) = 20 \]

Calculating each term:

\[ 15 + 2.5 = 20 \]

Adding these amounts together:

\[ 17.5 \neq 20 \]

Since \( 17.5 \) does not equal \( 20 \), this means that it is not possible for Santiago to have bought 10 board books and 5 soft cover books within the $20 budget.

Thus, the answer is no, Santiago could not have bought that combination of books.