A day at the Amusement Park

The admission fee at an amusement park is $7.50 for children and 16.00 for adults. On a certain day, 357 people entered the park, and the admission fees collected totaled $4,080.00. How many children and how many adults were admitted?

There were  children and  adults admitted into the park

Let's denote:
- $ x $ as the number of children admitted.
- $ y $ as the number of adults admitted.

We are given two pieces of information:
1. The total number of people is 357, so:
   \[
   x + y = 357
   \]
2. The total revenue collected from the admission fees is $4,080.00, where the admission fee is $7.50 for children and $16.00 for adults:
   \[
   7.50x + 16.00y = 4080
   \]

We now have a system of two equations:
1. $ x + y = 357 $
2. $ 7.50x + 16.00y = 4080 $

### Solving the system of equations:

#### Step 1: Solve the first equation for $ y $:
\[
y = 357 - x
\]

#### Step 2: Substitute $ y = 357 - x $ into the second equation:
\[
7.50x + 16(357 - x) = 4080
\]

#### Step 3: Expand and solve for $ x $:
\[
7.50x + 5712 - 16x = 4080
\]
\[
-8.50x + 5712 = 4080
\]
\[
-8.50x = 4080 - 5712
\]
\[
-8.50x = -1632
\]
\[
x = \frac{-1632}{-8.50} = 192
\]

So, 192 children were admitted.

#### Step 4: Substitute $ x = 192 $ back into the first equation to find $ y $:
\[
192 + y = 357
\]
\[
y = 357 - 192 = 165
\]

So, 165 adults were admitted.

### Final Answer:
- 192 children were admitted.
- 165 adults were admitted.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:
1. What if the adult admission fee increased by $4? How would the solution change?
2. If 50 more adults entered, how would the total revenue change?
3. What would the new total revenue be if the children's admission fee was reduced to $5?
4. How would the equations change if there were 400 people in the park?
5. If the park offered a discount of 10% on the total admission fees, what would the new total revenue be?

**Tip**: When solving systems of equations, substitution is useful when one equation is easily solved for a variable, while elimination is better when both equations are in standard form.

The admission fee at an amusement park is $7.50 for children and $16.00 for adults. On a certain day, 357 people entered the park, and the admission fees collected totaled $4,080.00. How many children and how many adults were admitted?

Learn how to solve a real-world problem involving a system of linear equations. Given the admission fees of $7.50 for children and $16.00 for adults, with 357 total attendees and $4,080.00 in collected revenue, calculate the number of children and adults admitted. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation