Question

the admission fee at an amusement park is $3.00 for children and $6.80 for adults. on a certain day, 299 people entered the park, and the admission fees collected totaled 1162 dollars. how many children and how many adults were admitted?​

Answer 1

Using a system of equations with the given admission prices and totals, we can find out there were 230 children and 69 adults admitted to the amusement park that day.

Step-by-step explanation:

To solve the problem of how many children and adults were admitted to the amusement park, we need to set up a system of linear equations based on the information given. We are told that the total number of people admitted is 299 and the total admission fees collected are $1162.

Let x represent the number of children and y represent the number of adults. We then have two equations:

1. x + y = 299 (the total number of people admitted)
2. 3.00x + 6.80y = 1162 (the total amount of money collected from admission fees)

Now, solve this system of equations. First, multiply the first equation by 3.00 to align the coefficient with the children's price in the second equation.

3.00x + 3.00y = 897

Subtract this new equation from the second one:

3.80y = 265

Now divide by 3.80:

y = 69.74, which we round down to 69 because the number of people must be whole. Therefore, there were 69 adults. Use y = 69 in the first equation to find x:

x + 69 = 299

x = 230

So there were 230 children.