To determine which equation models the situation described, we need to create an equation based on the given information:
1. Let [tex]\( m \)[/tex] represent the number of magazines Hugh bought.
2. Let [tex]\( b \)[/tex] represent the number of books Hugh bought.
3. Each magazine costs [tex]\( \$3.95 \)[/tex].
4. Each book costs [tex]\( \$8.95 \)[/tex].
5. Hugh spent a total of [tex]\( \$47.65 \)[/tex].
Here's how we can model the situation:
[tex]\[ \text{Cost of magazines} = 3.95m \][/tex]
[tex]\[ \text{Cost of books} = 8.95b \][/tex]
The total amount spent is the sum of the costs of magazines and books. Therefore, we can write the equation as:
[tex]\[ 3.95m + 8.95b = 47.65 \][/tex]
This equation states that the total cost of [tex]\( m \)[/tex] magazines and [tex]\( b \)[/tex] books equals [tex]\( \$47.65 \)[/tex].
Given the options:
1. [tex]\( m + b = 47.95 \)[/tex]
2. [tex]\( m + b = 60.55 \)[/tex]
3. [tex]\( 3.95m + 8.95b = 47.65 \)[/tex]
4. [tex]\( 8.95m + 3.95b = 47.65 \)[/tex]
The correct equation that models the situation is:
[tex]\[ 3.95m + 8.95b = 47.65 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
This equation takes into account the cost of magazines and books and the total amount spent by Hugh.
