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) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 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. Skip to navigation

Answer 1

To represent the situation mathematically, we can set up two equations based on the information provided.

1. Let \( a \) be the number of adult tickets sold and \( s \) be the number of student tickets sold.

2. The total cost of all tickets sold is given by:

   \[ 4a + 2.50s = 2820 \]

3. It is also mentioned that a total of 900 tickets were sold:

   \[ a + s = 900 \]

Now we have a system of equations:

1. \( 4a + 2.50s = 2820 \)
2. \( a + s = 900 \)

To solve for the number of adult and student tickets sold, we can start by isolating \( s \) in the second equation:

\[ s = 900 - a \]

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

\[ 4a + 2.50(900 - a) = 2820 \]

Distributing \( 2.50 \):

\[ 4a + 2250 - 2.50a = 2820 \]

Combining like terms:

\[ (4a - 2.50a) + 2250 = 2820 \]

\[ 1.50a + 2250 = 2820 \]

Subtracting 2250 from both sides:

\[ 1.50a = 2820 - 2250 \]

\[ 1.50a = 570 \]

Dividing both sides by 1.50:

\[ a = \frac{570}{1.50} = 380 \]

Now, use the value of \( a \) to find \( s \):

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

Final Answer:

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