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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.
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.
Option: 309, 4, 2820, a, 900, 390, 591, s, 2.50, 520, 380, 510, 6.5

Answer 1

Let's break down the problem step by step using the information given.

1. Cost Equation: We know that adult tickets cost $4 and student tickets cost $2.50, with the total revenue equaling $2,820. This can be modeled with the following equation:

   \[ 4a + 2.5s = 2820 \]

2. Ticket Quantity Equation: We also know that a total of 900 tickets were sold (both adult and student tickets). This can be modeled with the following equation:

   \[ a + s = 900 \]

Now, we have the system of equations:

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

Next, we can use this system of equations to solve for the number of adult tickets (\(a\)) and student tickets (\(s\)) sold.

Step 1: Solve the second equation for one variable

From the second equation:

\[ s = 900 - a \]

Step 2: Substitute into the first equation

Now substitute \(s\) from the second equation into the first equation:

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

Step 3: Simplify and solve for \(a\)

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:

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

Step 4: Find \(s\)

Now, use \(a = 380\) to find \(s\):

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

Final Results

Thus, the number of tickets sold is:

• Adult Tickets: \(380\)
• Student Tickets: \(520\)

Summary

To fill in the placeholders:

1. Equation for ticket cost: \[ 4a + 2.5s = 2820 \]
2. Equation for ticket quantity: \[ a + s = 900 \]
3. Final counts:
   • \(380\) adult tickets and \(520\) student tickets were sold.