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 hard cover books are $2.00 and soft cover books are $1.00. He picks out a variety of books and spends $30.

Question

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 hard cover books are $2.00 and soft cover books are $1.00. He picks out a variety of books and spends $30. 
A. Write a two-variable equation to represent this situation. Be sure to define the variables you use in your equation.

B. Is it possible that Santiago bought 10 hard cover books and 5 soft cover books? Use your equation from part A to check. Explain your answer( h \) is the number of hard cover books.
- $ s $ is the number of soft cover books.

Hard cover books cost $2.00 each, and soft cover books cost $1.00 each. Santiago spends a total of $30 on these books.

So, we can write an equation to show this. The equation is:

$$ 2h + 1s = 30 $$

This means that if you take the number of hard cover books ($ h $) and multiply it by $2 (because they cost $2 each), and then add that to the number of soft cover books ($ s $) multiplied by $1 (since they cost $1 each), the total has to equal $30.

That's how we can use this equation to figure out how many books Santiago bought+41++687

GPT-4o mini · Answer

A. To represent the situation with a two-variable equation, we define the variables as follows:

Let $ h $ be the number of hard cover books.
Let $ s $ be the number of soft cover books.

The cost of hard cover books is $2.00 each, and the cost of soft cover books is $1.00 each. Santiago spends a total of $30 on these books. Therefore, we can write the equation as:

\[ 2h + 1s = 30 \]

This equation models the total cost of the books Santiago purchased.

B. To check if it's possible that Santiago bought 10 hard cover books and 5 soft cover books, we will substitute $ h = 10 $ and $ s = 5 $ into the equation:

\[ 2(10) + 1(5) = 30 \]

Calculating the left side:

\[ 20 + 5 = 25 \]

Since $ 25 $ does not equal $ 30 $, this means that it is not possible for Santiago to have bought 10 hard cover books and 5 soft cover books. Therefore, the combination does not satisfy the equation.

In conclusion, the total amount spent by Santiago would need to match $30, and in this case, he only spent $25, which confirms that the combination of 10 hard cover books and 5 soft cover books is not valid based on the equation $ 2h + 1s = 30 $.