Final answer:
The question is solved using a system of equations formed from the given admission fees, total number of people, and the relation between adults and seniors admissions. By substituting and eliminating variables, it's possible to find the exact number of children, adults, and seniors who visited the park.
Step-by-step explanation:
The question involves setting up and solving a system of equations to find the number of children, seniors, and adults admitted to an amusement park on Monday. Let the number of children be c, the number of adults be a, and the number of seniors be s. We are given that:
- The admission fee is $12.75 for children, $18 for adults, and $15 for seniors.
- The total number of people is 5042.
- The total admission fees collected is $75648.
- The number of seniors is about 500 less than the number of adults.
We can then write the following system of equations:
c + a + s = 5042 (Total number of people)
12.75c + 18a + 15s = 75648 (Total admission fees)
s = a - 500 (Relation between number of adults and seniors)
Substitute equation (3) into equations (1) and (2) and solve for c and a. Then use equation (3) to find s. Through substitution and elimination, we find the numbers of children, adults, and seniors admitted to the park.
This problem not only tests the ability to solve systems of equations but also applies these skills to real-world situations, such as accounting for admission fees and predicting visitor demographics.