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.

Question

(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.

Answer 1

To set up the equations for the situation described, let's break it down step by step.

1. Equation for the total cost of tickets sold: The revenue from adult tickets is represented as \( 4a \) (where \( a \) is the number of adult tickets sold), and the revenue from student tickets is represented as \( 2.5s \) (where \( s \) is the number of student tickets sold). The total revenue is \( 2,820 \). Therefore, the equation will be:

   \[ 4a + 2.5s = 2820 \]

2. Equation for the total number of tickets sold: Since a total of 900 tickets were sold, we can express this as:

   \[ a + s = 900 \]

Now, we have a system of two equations:

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

To solve this system of equations for the number of adult and student tickets sold, we can use substitution or elimination.

Let's solve it using substitution:

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

\[ s = 900 - a \]

Now, substitute this expression for \( s \) into the first equation:

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

Distributing \( 2.5 \):

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

Combining like terms:

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

This simplifies to:

\[ 1.5a + 2250 = 2820 \]

Subtracting 2250 from both sides:

\[ 1.5a = 570 \]

Dividing by 1.5:

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

Now, substitute \( a \) back to find \( s \):

\[ s = 900 - 380 = 520 \]

Thus:

• Adult tickets sold: 380
• Student tickets sold: 520

Now, here is the completed response based on the input format you requested:

• Write an equation that represents this situation to find the cost of all adult and student tickets sold:

  Response area: \( 4a + 2.5s = 2820 \)

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

  Response area: \( a + s = 900 \)

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

  Response area: 380 adult tickets and 520 student tickets were sold.