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

Question

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 $.
make this like a 9th grader wrote it

GPT-4o mini · Answer

Sure! Here’s a simpler version that sounds more like a 9th grader wrote it:

To figure out how much money Santiago spent on books, we can use two variables. Let’s say:

$ h $ = the number of hard cover books.
$ s $ = the number of soft cover books.

Each hard cover book costs $2.00 and each soft cover book costs $1.00. Santiago spends a total of $30 on these books. So we can write this equation:

\[ 2h + 1s = 30 \]

This equation shows how much he spent on all the books.

Now, let’s see if it’s possible for Santiago to have bought 10 hard cover books and 5 soft cover books. We’ll plug in $ h = 10 $ and $ s = 5 $ into the equation:

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

Now let’s do the math on the left side:

\[ 20 + 5 = 25 \]

Since 25 does not equal 30, this means it’s not possible for Santiago to have bought 10 hard cover books and 5 soft cover books. So, that combination doesn’t work.

In summary, for Santiago’s total spending to match $30, the numbers he chose don’t add up right. He would only be spending $25 with that combo, which means 10 hard cover books and 5 soft cover books is not a valid option based on our equation $ 2h + 1s = 30 $.