Question

he admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 304 people entered the park, and the admission fees collected totaled $906. How many children and how many adults were admitted?

Answer 1

To solve the problem, set up a system of equations representing the total number of people admitted and the total admission fees collected. Use the elimination method to solve for the number of children and adults admitted. The solution is 124 children and 180 adults.

Step-by-step explanation:

To solve the problem, we can set up a system of equations:

Let x be the number of children admitted.

Let y be the number of adults admitted.

From the given information, we can write the following equations:

1. x + y = 304 (equation 1, representing the total number of people admitted)
2. 1.50x + 4.00y = 906 (equation 2, representing the total admission fees collected)

We can solve this system of equations using substitution or elimination method. Let's use the elimination method:

• Multiply equation 1 by 1.50 to make the coefficients of x in both equations equal:
• 1.50x + 1.50y = 456 (equation 3)
• Subtract equation 3 from equation 2:

1.50x + 4.00y - 1.50x - 1.50y = 906 - 456

2.50y = 450

Divide both sides of the equation by 2.50:

y = 180

Now substitute the value of y in equation 1:

x + 180 = 304

x = 304 - 180

x = 124

Therefore, 124 children and 180 adults were admitted to the amusement park.