Question
year;1, 2, 3, 4, 5
attendance; 8,255, 9,242, 10,704, 11,925, 13,268
This year, the first 30% of people attending the game will receive a raffle ticket. Of the people who receive raffle tickets, 1/5 will receive a small prize.
based on the data in the table, detirmine a reasonable estimate of the number of people who will attend this years game. Explain how you found this years estimate.
use your estimate to find the approximate number of people who receive a small prize at this years game
show your work.
attendance; 8,255, 9,242, 10,704, 11,925, 13,268
This year, the first 30% of people attending the game will receive a raffle ticket. Of the people who receive raffle tickets, 1/5 will receive a small prize.
based on the data in the table, detirmine a reasonable estimate of the number of people who will attend this years game. Explain how you found this years estimate.
use your estimate to find the approximate number of people who receive a small prize at this years game
show your work.
Answers
GPT-4o mini
To estimate the number of people attending this year's game, we will first look at the trend in attendance from previous years.
The attendance data given is:
- Year 1: 8,255
- Year 2: 9,242
- Year 3: 10,704
- Year 4: 11,925
- Year 5: 13,268
Next, let's calculate the year-over-year change in attendance:
- Year 1 to Year 2: 9,242 - 8,255 = 987
- Year 2 to Year 3: 10,704 - 9,242 = 1,462
- Year 3 to Year 4: 11,925 - 10,704 = 1,221
- Year 4 to Year 5: 13,268 - 11,925 = 1,343
Now, let's calculate the average increase in attendance over the 4 years:
\[
\text{Average increase} = \frac{987 + 1,462 + 1,221 + 1,343}{4} = \frac{4,013}{4} = 1,003.25
\]
Since the average increase is approximately 1,003, we can estimate this year's attendance by adding this average increase to the previous year's (Year 5) attendance:
\[
\text{Estimated attendance for Year 6} = 13,268 + 1,003 = 14,271
\]
Now that we have an estimate of 14,271 for this year's attendance, we can proceed to determine the number of people who will receive a small prize.
First, we calculate 30% of the estimated attendance:
\[
30\% \text{ of } 14,271 = 0.30 \times 14,271 = 4,281.3 \approx 4,281 \text{ (rounded down)}
\]
Next, we need to find out how many of those ticket holders will receive a small prize, which is 1/5 of the raffle ticket holders:
\[
\text{Number of people receiving a small prize} = \frac{4,281}{5} = 856.2 \approx 856 \text{ (rounded down)}
\]
Therefore, the reasonable estimate of the number of people who will attend this year's game is **14,271**, and the approximate number of people who receive a small prize at this year's game is **856**.
The attendance data given is:
- Year 1: 8,255
- Year 2: 9,242
- Year 3: 10,704
- Year 4: 11,925
- Year 5: 13,268
Next, let's calculate the year-over-year change in attendance:
- Year 1 to Year 2: 9,242 - 8,255 = 987
- Year 2 to Year 3: 10,704 - 9,242 = 1,462
- Year 3 to Year 4: 11,925 - 10,704 = 1,221
- Year 4 to Year 5: 13,268 - 11,925 = 1,343
Now, let's calculate the average increase in attendance over the 4 years:
\[
\text{Average increase} = \frac{987 + 1,462 + 1,221 + 1,343}{4} = \frac{4,013}{4} = 1,003.25
\]
Since the average increase is approximately 1,003, we can estimate this year's attendance by adding this average increase to the previous year's (Year 5) attendance:
\[
\text{Estimated attendance for Year 6} = 13,268 + 1,003 = 14,271
\]
Now that we have an estimate of 14,271 for this year's attendance, we can proceed to determine the number of people who will receive a small prize.
First, we calculate 30% of the estimated attendance:
\[
30\% \text{ of } 14,271 = 0.30 \times 14,271 = 4,281.3 \approx 4,281 \text{ (rounded down)}
\]
Next, we need to find out how many of those ticket holders will receive a small prize, which is 1/5 of the raffle ticket holders:
\[
\text{Number of people receiving a small prize} = \frac{4,281}{5} = 856.2 \approx 856 \text{ (rounded down)}
\]
Therefore, the reasonable estimate of the number of people who will attend this year's game is **14,271**, and the approximate number of people who receive a small prize at this year's game is **856**.