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QuestionMathematics

Why are there 52 weeks in a year and not 48 weeks, given that there are only 4 weeks per month (4 x 12 = 48)?
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Step 1:
I'll solve this problem step by step, explaining the discrepancy between calendar weeks and months.

Step 2:
: Understanding Month Length

Most months are actually longer than exactly 4 weeks. While 4 × 12 = 48 weeks would seem logical, the actual calculation is more nuanced.

Step 3:
: Precise Month Length Calculation

A typical month ranges between 28 and 31 days: - 28 days (February in non-leap years) - 30 days (April, June, September, November) - 31 days (January, March, May, July, August, October, December)

Step 4:
: Week Length Conversion

1 \text{ week} = 7 \text{ days}

Step 5:
: Average Month Length

Average month length: $$\frac{(28 + 30 + 31 \times 7)}{12} \approx 30.44 \text{ days}

Step 6:
: Weeks per Year Calculation

365.25 \text{ days} \div 7 \text{ days per week} \approx 52.18 \text{ weeks}

Final Answer

There are 52 weeks in a year because the average month is slightly longer than exactly 4 weeks, resulting in a total of approximately 52.18 weeks annually.