Question

The admission fee at an amusement park is $4.25 for children and $5.40 for adults. On a certain day, 280 people entered the park, and the admission fees collected totaled 1397 dollars. How many children and how many adults were admitted?

Answer 1

Using algebraic methods to solve a system of linear equations, we find that 100 children and 180 adults were admitted to the amusement park, with children's admission at $4.25, and adults' at $5.40.

Step-by-step explanation:

The student's question involves a system of linear equations, which is a concept in algebra used to solve problems with multiple constraints, commonly found within the subject of mathematics. In this scenario, the total number of people (280) and the total amount of admission fees ($1397) are the constraints. We have two unknowns: the number of children (C) and the number of adults (A). We can represent this problem with the following equations:

1) C + A = 280 (equation representing the total number of people)

2) 4.25C + 5.40A = 1397 (equation representing the total collected fees)

To solve this system, we can use substitution or elimination. Here, elimination might be the simpler approach. For example, if we multiply the first equation by 4.25, we can then subtract the new equation from the second to eliminate C and solve for A:

4.25C + 4.25A = 1190 (the first equation multiplied by 4.25)

4.25C + 5.40A = 1397 (original second equation)

This simplifies to:

1.15A = 207

Divide by 1.15 and we find that A (number of adults) is 180. Subtract this from 280, and we have C (number of children) = 100.

Therefore, there were 100 children and 180 adults admitted to the park on that day.