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: Understanding the Question:
The problem asks to calculate the average number of visitors per day for a month of 30 days, given different average visitor numbers for Sundays and other days, and knowing that the month starts on a Sunday.

Step 2: Key Formula or Approach:
Average = $\frac{\text{Total number of visitors}}{\text{Total number of days}}$.
1. Determine the number of Sundays in the month.
2. Determine the number of "other days" in the month.
3. Calculate the total visitors for Sundays.
4. Calculate the total visitors for "other days".
5. Sum these to get the total visitors for the month.

Step 3: Detailed Explanation:
Given:
- Total days in the month = 30.
- Month begins with a Sunday.
- Average visitors on Sundays = 510.
- Average visitors on other days = 240.
1. Number of Sundays in the month:
Since the month starts on a Sunday, the Sundays will fall on days: 1, 8, 15, 22, 29.
Number of Sundays = 5.
2. Number of other days:
Number of other days = Total days - Number of Sundays = $30 - 5 = 25$.
3. Total visitors on Sundays:
Total Sunday visitors = $5 \text{ Sundays} \times 510 \text{ visitors/Sunday} = 2550$.
4. Total visitors on other days:
Total other day visitors = $25 \text{ days} \times 240 \text{ visitors/day} = 6000$.
5. Total visitors for the month:
Total visitors = Total Sunday visitors + Total other day visitors = $2550 + 6000 = 8550$.
6. Average number of visitors per day:
Average = $\frac{\text{Total visitors}}{\text{Total days}} = \frac{8550}{30} = \frac{855}{3} = 285$.

Step 4: Final Answer:
The average number of visitors per day is 285.

Answer 2

Instead of adding up the Sunday total and the other-day total separately, we can use a baseline-and-adjustment shortcut: assume every day in the month had the "other days" average of 240 visitors, and then add back the extra visitors that Sundays bring in.

First, find the number of Sundays. The month has 30 days and begins on a Sunday, so Sundays fall on days 1, 8, 15, 22, and 29, giving 5 Sundays in total, and 25 non-Sunday days.

If every one of the 30 days had 240 visitors, the baseline total would be:

\[ 30 \times 240 = 7200 \]

But each Sunday actually has 510 visitors instead of 240, an excess of \(510-240=270\) visitors per Sunday. Over the 5 Sundays, this adds an extra:

\[ 5 \times 270 = 1350 \]

Adding this adjustment to the baseline gives the true total number of visitors for the month:

\[ 7200+1350 = 8550 \]

Dividing by the 30 days in the month gives the average:

\[ \frac{8550}{30} = 285 \]

Checking the other options: 290, 297, and 305 would all require either a different Sunday count or a miscalculated excess-per-Sunday figure; none of them arise from the actual 5-Sunday, 270-visitor-excess breakdown of this month.

Therefore, the correct answer is 285.