Let's go through the problem step by step to determine the correct equation that models the given situation.
1. First, identify the variables and their respective costs from the problem:
- Let [tex]\( m \)[/tex] represent the number of magazines.
- Each magazine costs \[tex]$3.95.
- Let \( b \) represent the number of books.
- Each book costs \$[/tex]8.95.
2. Next, understand the total expenditure mentioned in the problem:
- Hugh spent a total of \$47.65.
3. To form an equation, we need to represent the total cost in terms of the number of magazines ([tex]\( m \)[/tex]) and books ([tex]\( b \)[/tex]).
- The cost of [tex]\( m \)[/tex] magazines is [tex]\( 3.95m \)[/tex].
- The cost of [tex]\( b \)[/tex] books is [tex]\( 8.95b \)[/tex].
4. Since the total expenditure is the sum of the cost of the magazines and the books, we can write the equation as:
[tex]\[
3.95m + 8.95b = 47.65
\][/tex]
5. Finally, let's verify the provided options:
- Option 1: [tex]\( m + b = 47.95 \)[/tex]
This option suggests that the sum of the number of magazines and books equals 47.95, which does not correctly represent the given costs and total expenditure.
- Option 2: [tex]\( m + b = 60.55 \)[/tex]
This option also does not correctly combine the costs and the total amount spent.
- Option 3: [tex]\( 3.95m + 8.95b = 47.65 \)[/tex]
This option matches our derived equation and accurately represents the relationship described in the problem.
- Option 4: [tex]\( 8.95m + 3.95b = 47.65 \)[/tex]
This option incorrectly assigns the cost per unit to the wrong variable (m for books and b for magazines), so it's not correct.
The correct equation that models the situation given in the problem is:
[tex]\[
3.95m + 8.95b = 47.65
\][/tex]
