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

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

Find the number of books [tex]\( b \)[/tex].



Answer :

GinnyAnswer
Certainly! Let's break down this problem step by step to determine how many books Hugh bought.

1. Identify the cost of each magazine and book:
- Cost per magazine = [tex]$3.95 - Cost per book = $[/tex]8.95

2. Identify the total amount spent:
- Total amount spent = $47.65

3. Identify the number of magazines purchased:
- Number of magazines bought = 3

4. Calculate the total cost of the magazines:
[tex]\[ \text{Total cost of magazines} = \text{Number of magazines} \times \text{Cost per magazine} \][/tex]
[tex]\[ \text{Total cost of magazines} = 3 \times 3.95 = 11.85 \][/tex]

5. Calculate the remaining amount after buying the magazines:
[tex]\[ \text{Remaining amount} = \text{Total amount spent} - \text{Total cost of magazines} \][/tex]
[tex]\[ \text{Remaining amount} = 47.65 - 11.85 = 35.80 \][/tex]

6. Calculate the number of books bought:
[tex]\[ \text{Number of books bought} = \frac{\text{Remaining amount}}{\text{Cost per book}} \][/tex]
[tex]\[ \text{Number of books bought} = \frac{35.80}{8.95} = 4 \][/tex]

Hence, Hugh bought 4 books.

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