Question

A ballpark sells two types of tickets: a reserved seat for $14
and a box seat for $18
. Yesterday, the ballpark sold a total of 2820
tickets for a total of 44280.
.
Write the system of equations to find the number of reserved seats and box seats sold. Let x
be the number of reserved seats sold and y
be the number of box seats sold. Do not solve.

Answer 1

To create a system of equations based on the information provided, we can define:

- \( x \) as the number of reserved seats sold
- \( y \) as the number of box seats sold

From the problem statement, we have two key pieces of information:

1. The total number of tickets sold (both reserved and box seats) is 2820.
2. The total revenue from the ticket sales is $44280.

Using this information, we can set up the following equations:

1. For the total number of tickets:
\[
x + y = 2820
\]

2. For the total revenue generated from the ticket sales:
\[
14x + 18y = 44280
\]

Thus, the system of equations is:

\[
\begin{cases}
x + y = 2820 \\
14x + 18y = 44280
\end{cases}
\]