Let's begin by breaking down the problem step-by-step to determine how many books Hugh bought.
1. Identify given quantities:
- Cost of each magazine: \$3.95
- Cost of each book: \$8.95
- Total amount spent: \$47.65
- Number of magazines bought: 3
2. Write down the equation:
Given the cost of magazines and books, and the total amount spent, the equation is:
[tex]\[
3.95m + 8.95b = 47.65
\][/tex]
Here, \( m \) is the number of magazines, and \( b \) is the number of books. We know \( m = 3 \).
3. Substitute the number of magazines into the equation:
Substitute \( m = 3 \) into the equation:
[tex]\[
3.95 \cdot 3 + 8.95b = 47.65
\][/tex]
4. Calculate the total cost for the magazines:
[tex]\[
3.95 \cdot 3 = 11.85
\][/tex]
5. Subtract the cost of the magazines from the total amount spent to find the remaining money for the books:
[tex]\[
47.65 - 11.85 = 35.80
\][/tex]
6. Calculate the number of books bought by dividing the remaining money by the cost of each book:
[tex]\[
b = \frac{35.80}{8.95}
\][/tex]
7. Perform the division:
[tex]\[
b = 4
\][/tex]
Thus, Hugh bought [tex]\(\boxed{4}\)[/tex] books.
