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Hugh bought some magazines that cost [tex]$\$[/tex]3.95[tex]$ each and some books that cost $[/tex]\[tex]$8.95$[/tex] each. He spent a total of [tex]$\$[/tex]47.65[tex]$. Let $[/tex]m[tex]$ represent the number of magazines and $[/tex]b$ represent the number of books. Which equation models the situation?

A. [tex]$m + b = 47.95$[/tex]
B. [tex]$m + b = 60.55$[/tex]
C. [tex]$3.95m + 8.95b = 47.65$[/tex]
D. [tex]$8.95m + 3.95b = 47.65$[/tex]


Sagot :

To determine which equation accurately represents the financial situation described, we need to consider the costs associated with the magazines and books Hugh bought.

1. Cost of each magazine: \$3.95
2. Cost of each book: \$8.95
3. Total amount spent: \$47.65
4. Let \( m \) be the number of magazines and \( b \) be the number of books.

From these points, we can establish an equation that reflects the given situation.

The total cost for all magazines can be calculated as:
[tex]\[ \text{Cost of magazines} = 3.95m \][/tex]

The total cost for all books can be calculated as:
[tex]\[ \text{Cost of books} = 8.95b \][/tex]

Since Hugh spent a total of \$47.65 on magazines and books, we can combine the individual costs to form the total cost equation:
[tex]\[ 3.95m + 8.95b = 47.65 \][/tex]

Let's now evaluate the options provided to see which one matches our derived equation:
- \( m + b = 47.95 \)
- \( m + b = 60.55 \)
- \( 3.95m + 8.950 = 47.65 \)
- \( 8.95m + 3.95b = 47.65 \)

The correct equation, according to our derived expression, is:
[tex]\[ 3.95m + 8.95b = 47.65 \][/tex]

So the correct answer is:
[tex]\[ 3.95m + 8.95b = 47.65 \][/tex]