Question

The admission fee at an amusement park is a dollar fifty for children and $4 for adults on a certain day 238 people entered the park and the admission fees collected totaled 682.00 dollars how many children and how many adults were admitted

Answer 1

The question is solved by setting up a system of linear equations and using the substitution method to find that 108 children and 130 adults were admitted to the amusement park.

Step-by-step explanation:

The problem presented is a classic example of a system of linear equations. We are given the number of people entering an amusement park and the total admission fees collected. We need to determine how many children and how many adults were admitted.

Let C represent the number of children and A represent the number of adults. We can create the following system of equations based on the information given:

• C + A = 238 (equation 1: representing the total number of people)
• 1.50C + 4A = 682 (equation 2: representing the total cost)

To solve this system, we can use a method such as substitution or elimination. For simplicity, we'll use substitution.

1. Multiply equation 1 by 1.50 to align the children's cost with equation 2, resulting in 1.50C + 1.50A = 357.
2. Subtract this new equation from equation 2. This yields: 4A - 1.50A = 682 - 357, which simplifies to 2.5A = 325.
3. Divide both sides by 2.5 to find the number of adults: A = 130.
4. Substitute the value of A back into equation 1 to find the number of children: C + 130 = 238, so C = 108.

Therefore, 108 children and 130 adults were admitted to the park.