Question

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

• A. 285
• B. 290
• C. 297
• D. 305

Hint:

Carefully count the number of specific days (e.g., Sundays) in the given month, especially when the starting day is specified. Avoid making assumptions about the number of weekend days if not explicitly stated.

Answer 1

The Correct Option is C

Step 1: Out of the 30 days, 5 are Sundays (days 1, 8, 15, 22, 29) and the remaining 25 are other days, since the month begins on a Sunday.

Step 2: Write the overall average as a weighted average of the two daily averages, weighted by how many days of each type there are: \( \text{Average} = \frac{5}{30}(510) + \frac{25}{30}(240) \).

Step 3: Simplify each term: \( \frac{5}{30}(510) = \frac{1}{6}(510) = 85 \), and \( \frac{25}{30}(240) = \frac{5}{6}(240) = 200 \). Add them together: \(85+200=285\).
\[ \boxed{285} \]