Question

Last Saturday.1.750 people attended an event at Fairway Gardens.The admission fee was 3.50 for children and 8.00 for adults . If the total amount of money collected at the event was 9,860 how many children and how many adults attended the event?
Equation 1: __ Equation 2: adults and __ children attended the event.

Answer 1

To solve this problem, we need to set up a system of equations based on the given information and then solve them.

Let's define:
- \( x \) as the number of children who attended the event.
- \( y \) as the number of adults who attended the event.

We are given two pieces of information:
1. The total number of people who attended the event is 1,750.
2. The total amount of money collected from the admission fees is $9,860.

Using these pieces of information, we can create the following two equations:

1. The sum of the number of children and adults is 1,750:
\[
x + y = 1750
\]

2. The total income from children (\(3.50 \times x\)) and adults (\(8.00 \times y\)) amounts to $9,860:
\[
3.50x + 8.00y = 9860
\]

We now have a system of two equations:
\[
\begin{align}
x + y &= 1750 \quad \text{(Equation 1)} \\
3.50x + 8.00y &= 9860 \quad \text{(Equation 2)}
\end{align}
\]

To solve this system, we can use the substitution method or the elimination method. Here, we'll use substitution.

First, solve Equation 1 for \( y \):
\[
y = 1750 - x
\]

Now, substitute this expression for \( y \) into Equation 2:
\[
3.50x + 8.00(1750 - x) = 9860
\]

Simplify and solve for \( x \):
\[
3.50x + 14000 - 8.00x = 9860
\]
\[
3.50x - 8.00x = 9860 - 14000
\]
\[
-4.50x = -4140
\]
\[
x = \frac{4140}{4.50}
\]
\[
x = 920
\]

So, \( x = 920 \). This means there were 920 children at the event.

Now, substitute \( x = 920 \) back into Equation 1 to find \( y \):
\[
y = 1750 - 920
\]
\[
y = 830
\]

Therefore, 830 adults attended the event.

So, the final answer is:
- Equation 1: \( x + y = 1750 \)
- Equation 2: \( 3.50x + 8.00y = 9860 \)

And the number of attendees:
- There were 920 children and 830 adults who attended the event.