Bot GPT 4-o mini Let's denote the number of board books Santiago purchased as \( b \) and the number of soft cover books as \( s \). We are given the following two equations based on the information about the total number of books and the total cost:
- \( b + s = 34 \) (equation for the total number of books)
- \( 1.50b + 0.50s = 20 \) (equation for the total cost)
We can simplify the second equation by multiplying everything by 2 to avoid decimals:
\[ 3b + s = 40 \quad \text{(equation 2)} \]
Now we have the system of equations:
- \( b + s = 34 \)
- \( 3b + s = 40 \)
Next, we can solve for \( s \) in the first equation:
\[ s = 34 - b \]
Now, substitute \( s \) in the second equation:
\[ 3b + (34 - b) = 40 \]
Combine like terms:
\[ 3b - b + 34 = 40 \] \[ 2b + 34 = 40 \]
Subtract 34 from both sides:
\[ 2b = 6 \]
Divide by 2:
\[ b = 3 \]
Now substitute \( b \) back into the equation for \( s \):
\[ s = 34 - 3 = 31 \]
Thus, Santiago purchased \( 3 \) board books and \( 31 \) soft cover books.
So, the correct solution is 3 board books and 31 soft cover books.
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