Answer:
(126, 101), (127, 100), (128, 99).
Explanation:
The profit from selling one adult ticket is $10.00 and from selling one children's ticket is $5.00.
The total profit from selling A adult tickets and C children's tickets can be represented as 10A + 5C.
The goal is to find combinations of A and C that meet the following conditions:
10A + 5C >= 3750
A + C <= 500
One way to solve this problem is to use a brute force approach and try different values of A and C until we find three combinations that meet the conditions. Another way is to use a more efficient method and find the values of A and C that maximize the number of adult tickets while still meeting the profit and seating limit conditions.
Let's start by finding the maximum number of adult tickets that can be sold while still meeting the profit goal:
10A + 5C >= 3750
10A >= 3750 - 5C
A >= 375 - 0.5C
Since C must be an integer, we can round down the value of A to the nearest integer.
For example, if C = 100, then A >= 125. If we round down A to 125, then the profit from selling 125 adult tickets and 100 children's tickets would be:
10 * 125 + 5 * 100 = 1250 + 500 = 1750
which is less than the profit goal of 3750.
If we increase C by 1, then A would increase by 0.5, and the profit would increase by 5.
So, to reach the profit goal, we need to increase C until the profit is at least 3750.
Let's try C = 101. Then A >= 125.5, which we can round down to 126.
The profit from selling 126 adult tickets and 101 children's tickets would be:
10 * 126 + 5 * 101 = 1260 + 505 = 1765
which is greater than or equal to the profit goal of 3750.
So, the first combination of adult and children's tickets that meets the profit and seating limit conditions is (126, 101).
We can repeat the same process to find the second and third combinations.
For example, the second combination could be (127, 100), and the third combination could be (128, 99).
The final answer is (126, 101), (127, 100), (128, 99).