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Answer :
To help solve the problem, let's break it down step by step:
1. Calculate the miles Pierre runs each day:
Pierre runs a total of 12 miles each week, and he runs 4 days a week. To find out how many miles he runs each day, we divide the total weekly miles by the number of days he runs:
[tex]\[
\text{Miles per day} = \frac{12 \text{ miles per week}}{4 \text{ days per week}} = 3 \text{ miles per day}
\][/tex]
2. Convert miles to laps:
Since it takes 8 laps of the track to equal a mile, we multiply the miles Pierre runs each day by the number of laps per mile to find out how many laps he runs each day:
[tex]\[
\text{Laps per day} = 3 \text{ miles per day} \times 8 \text{ laps per mile} = 24 \text{ laps per day}
\][/tex]
3. Determine the correct equation to solve this problem:
We need an equation that reflects the calculation we just made. We know that Pierre runs 3 miles per day and it takes 8 laps for each mile, which leads us to:
[tex]\[
\text{Laps per day} = 3 \times 8
\][/tex]
This matches with option (C) [tex]\(y = 3 \times 8\)[/tex].
Therefore, the correct equation is [tex]\(y = 3 \times 8\)[/tex], and Pierre runs 24 laps each day.
1. Calculate the miles Pierre runs each day:
Pierre runs a total of 12 miles each week, and he runs 4 days a week. To find out how many miles he runs each day, we divide the total weekly miles by the number of days he runs:
[tex]\[
\text{Miles per day} = \frac{12 \text{ miles per week}}{4 \text{ days per week}} = 3 \text{ miles per day}
\][/tex]
2. Convert miles to laps:
Since it takes 8 laps of the track to equal a mile, we multiply the miles Pierre runs each day by the number of laps per mile to find out how many laps he runs each day:
[tex]\[
\text{Laps per day} = 3 \text{ miles per day} \times 8 \text{ laps per mile} = 24 \text{ laps per day}
\][/tex]
3. Determine the correct equation to solve this problem:
We need an equation that reflects the calculation we just made. We know that Pierre runs 3 miles per day and it takes 8 laps for each mile, which leads us to:
[tex]\[
\text{Laps per day} = 3 \times 8
\][/tex]
This matches with option (C) [tex]\(y = 3 \times 8\)[/tex].
Therefore, the correct equation is [tex]\(y = 3 \times 8\)[/tex], and Pierre runs 24 laps each day.
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