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12 Nov 2024, 03:45
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Maximum: 60
Minimum: 20
A certain number of people visited an amusement park on a specific day, which featured three rides: the Ferris Wheel, Classic Wooden Rollercoaster, and Merry-Go-Round, costing $1, $2, and $3 per ride, respectively.
Each person spent an average of $2 per ride, and the total money spent was $120. Every person took at least one ride and did not repeat any of the rides.
Based on this information, select for Maximum the greatest possible number of visitors and for Minimum the smallest possible number of visitors who could have visited the park. Make only two selections, one in each column.
Each person spent an average of $2 per ride, and the total money spent was $120. Every person took at least one ride and did not repeat any of the rides.
Based on this information, select for Maximum the greatest possible number of visitors and for Minimum the smallest possible number of visitors who could have visited the park. Make only two selections, one in each column.
| Maximum | Minimum | |
| 10 | ||
| 15 | ||
| 20 | ||
| 30 | ||
| 60 | ||
| 120 |
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Official Answer
Maximum: 60
Minimum: 20
12 Nov 2024, 03:45
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Official Solution:
Each person spending an average of $2 per ride implies the following three scenariois:
• A person could have taken all three rides ($1 + $2 + $3 = $6 total), resulting in an average of $2 per ride.
• A person could have taken the $1 and $3 rides ($1 + $3 = $4 total), again averaging $2 per ride.
• A person could have taken only the $2 ride.
Since the total spending was $120, the minimum number of people occurs when the maximum spending per person ($6) is achieved. This results in 120/6 = 20 people, meaning all 20 people took each of the three rides once. Conversely, the maximum number of people occurs when the minimum spending per person ($2) is achieved. This results in 120/2 = 60 people, meaning all 60 people took only the $2 ride once.
Correct answer:
Maximum "60"
Minimum "20"
bb
Each person spending an average of $2 per ride implies the following three scenariois:
• A person could have taken all three rides ($1 + $2 + $3 = $6 total), resulting in an average of $2 per ride.
• A person could have taken the $1 and $3 rides ($1 + $3 = $4 total), again averaging $2 per ride.
• A person could have taken only the $2 ride.
Since the total spending was $120, the minimum number of people occurs when the maximum spending per person ($6) is achieved. This results in 120/6 = 20 people, meaning all 20 people took each of the three rides once. Conversely, the maximum number of people occurs when the minimum spending per person ($2) is achieved. This results in 120/2 = 60 people, meaning all 60 people took only the $2 ride once.
Correct answer:
Maximum "60"
Minimum "20"
14 Nov 2024, 03:37
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Case 1 : Maximise Number of People (n) =x+y+z
Each person spent an average of 2 per ride on that day and the total amount of money spent combined was 120. Each person took at least one ride and did not take the same ride twice.
x+2y+3z=120
(x+2y+3z)/n = 2
=> 120/n= 2
=> n = 60
this is the max people.
Case 2: Minimum Number of People (n)
To minimize the number of people, each person should spend as much as possible within the conditions given.
If each person took all three rides (Ferris wheel, Classic wooden rollercoaster, and Merry-go-round) for a total cost of 1 + 2 + 3 = 6, we get:
n = 120/6= 20
So, the minimum number of people who could have visited the park is 20!
Each person spent an average of 2 per ride on that day and the total amount of money spent combined was 120. Each person took at least one ride and did not take the same ride twice.
x+2y+3z=120
(x+2y+3z)/n = 2
=> 120/n= 2
=> n = 60
this is the max people.
Case 2: Minimum Number of People (n)
To minimize the number of people, each person should spend as much as possible within the conditions given.
If each person took all three rides (Ferris wheel, Classic wooden rollercoaster, and Merry-go-round) for a total cost of 1 + 2 + 3 = 6, we get:
n = 120/6= 20
So, the minimum number of people who could have visited the park is 20!
