Question

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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)
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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.

Response area a + Response area s = Response area

900 tickets are sold for the spring fling. Write an equation to represent this situation.

a + Response area = Response area

Use the above system of equations to determine how many adult and student tickets were sold.

Response area adult tickets and Response area student tickets were sold.

2.50
4
a
591
309
2820
510
6.5
900
520
39
s
380

Answer 1

To set up the equations based on the information given about ticket sales for the Spring Fling, we'll use the following variables:

- Let \( a \) represent the number of adult tickets sold.
- Let \( s \) represent the number of student tickets sold.

### 1. Revenue Equation

The total revenue from ticket sales can be represented as:

\[
4a + 2.5s = 2820
\]

This equation states that the total income from adult tickets (4 times the number of adult tickets sold) plus the total income from student tickets (2.5 times the number of student tickets sold) equals a total of $2,820.

### 2. Total Tickets Equation

We know that a total of 900 tickets were sold, which can be represented as:

\[
a + s = 900
\]

### System of Equations

We now have the following system of equations:

1. \( 4a + 2.5s = 2820 \)
2. \( a + s = 900 \)

### Solving the System of Equations

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

**Step 1: Solve for \( s \) using the second equation:**

\[
s = 900 - a
\]

**Step 2: Substitute \( s \) into the first equation:**

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

**Step 3: Distribute \( 2.5 \):**

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

**Step 4: Combine like terms:**

\[
(4 - 2.5)a + 2250 = 2820
\]
\[
1.5a + 2250 = 2820
\]

**Step 5: Isolate \( a \):**

\[
1.5a = 2820 - 2250
\]
\[
1.5a = 570
\]
\[
a = \frac{570}{1.5} = 380
\]

**Step 6: Substitute \( a \) back to find \( s \):**

\[
s = 900 - 380 = 520
\]

### Final Result

- **Adult tickets sold:** \( 380 \)
- **Student tickets sold:** \( 520 \)

### Summary Inputs

1. **Revenue Equation:**
- \( 4a + 2.5s = 2820 \)

2. **Total Tickets Equation:**
- \( a + s = 900 \)

3. **Final Ticket Counts:**
- Adult tickets sold: **380**
- Student tickets sold: **520**