Question

Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.

Answer 1

so how many adult and student tickets were sold

Answer 2

900 tickets were sold

Answer 3

To represent the situation, we can set up an equation based on the total revenue generated from selling adult and student tickets.

Let:
- \( a \) = number of adult tickets sold
- \( s \) = number of student tickets sold

The cost for each adult ticket is $4, and the cost for each student ticket is $2.50. The total revenue from all tickets sold is $2,820.

The equation representing this situation is:

\[
4a + 2.5s = 2820
\]

This equation can be used to find the number of adult and student tickets sold.

Answer 4

To determine the number of adult and student tickets sold, we need an additional piece of information, such as the total number of tickets sold or a specific relationship between the numbers of adult and student tickets.

However, if we only have the equation \( 4a + 2.5s = 2820 \), we can express one variable in terms of another, but we cannot find unique values for \( a \) and \( s \) without additional information.

For example, if we wanted to express the number of student tickets in terms of the number of adult tickets, we could rearrange the equation:

\[
2.5s = 2820 - 4a
\]

\[
s = \frac{2820 - 4a}{2.5}
\]

This means you can choose a specific value for \( a \) (the number of adult tickets) and calculate the corresponding value for \( s \) (the number of student tickets).

If you have more information (like the total number of tickets sold), please provide it, and I can help calculate the specific numbers for \( a \) and \( s \).

Answer 5

Great! Now we have two equations to work with:

1. The revenue equation:
\[
4a + 2.5s = 2820
\]

2. The total tickets sold equation:
\[
a + s = 900
\]

Now we can solve this system of equations.

First, we can express \( s \) in terms of \( a \) from the second equation:

\[
s = 900 - a
\]

Next, we substitute this expression for \( s \) into the revenue equation:

\[
4a + 2.5(900 - a) = 2820
\]

Now, distribute \( 2.5 \):

\[
4a + 2250 - 2.5a = 2820
\]

Combine like terms:

\[
(4 - 2.5)a + 2250 = 2820
\]

\[
1.5a + 2250 = 2820
\]

Now, isolate \( a \):

\[
1.5a = 2820 - 2250
\]

\[
1.5a = 570
\]

Now, divide by 1.5:

\[
a = \frac{570}{1.5} = 380
\]

Now that we have \( a \), we can find \( s \):

\[
s = 900 - a = 900 - 380 = 520
\]

So, the final numbers of tickets sold are:
- Adult tickets sold (\( a \)): **380**
- Student tickets sold (\( s \)): **520**