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. (7 points) 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. a + S = 900 tickets are sold for the spring fling. Write an equation to represent this situation. a +! Use the above system of equations to determine how many adult and student tickets were sold. adult tickets and student tickets were sold. :: 390 :: 2820 :: 2.50 :: 510 :: 309 :: 4 :: 900 ":a :: 591 :: 380 :: 6.5 :: 520

Answer 1

To solve the problem, we first need to set up a system of equations based on the information provided.

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

From the problem, we know two things:

1. The total revenue from ticket sales is $2,820. The adult tickets cost $4 and student tickets cost $2.50, which gives us the first equation:
\[
4a + 2.5s = 2820
\]

2. The total number of tickets sold is 900, which gives us the second equation:
\[
a + s = 900
\]

Now we have the system of equations:
1. \( 4a + 2.5s = 2820 \)
2. \( a + s = 900 \)

Next, we can solve this system of equations to find the values of \( a \) and \( s \).

### Step 1: Solve the second equation for \( s \)
From the second equation, we can express \( s \) in terms of \( a \):
\[
s = 900 - a
\]

### Step 2: Substitute \( s \) into the first equation
Now, substitute \( s \) into the first equation:
\[
4a + 2.5(900 - a) = 2820
\]

### Step 3: Distribute and combine like terms
\[
4a + 2250 - 2.5a = 2820
\]

Combine like terms:
\[
(4 - 2.5)a + 2250 = 2820
\]
\[
1.5a + 2250 = 2820
\]

### Step 4: Isolate \( a \)
Subtract 2250 from both sides:
\[
1.5a = 2820 - 2250
\]
\[
1.5a = 570
\]

Now divide by 1.5:
\[
a = \frac{570}{1.5} = 380
\]

### Step 5: Find \( s \) using the value of \( a \)
Now substitute \( a = 380 \) back into the equation \( s = 900 - a \):
\[
s = 900 - 380 = 520
\]

### Conclusion
The number of adult tickets sold is \( 380 \) and the number of student tickets sold is \( 520 \). Thus, the solution to the problem is:
- Adult tickets sold: **380**
- Student tickets sold: **520**