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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]\$47.65[/tex]. If Hugh bought 3 magazines, how many books did he buy?

The equation that models the problem is [tex]3.95m + 8.95b = 47.65[/tex], where [tex]m[/tex] is the number of magazines and [tex]b[/tex] is the number of books.

[tex]\square[/tex] books


Sagot :

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.
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