Use your graphing calculator: Desmos Graphing Calculator LinkGeorgia 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 area900 tickets are sold for the spring fling. Write an equation to represent this situation.a + Response area = Response areaUse 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.s2.505913095106.52820900520390380a4

Answer 1

To model the scenario described, we can set up two equations based on the information about ticket sales.

1. Cost Equation: Each adult ticket costs $4 and each student ticket costs $2.50. The total revenue from ticket sales is $2,820. This gives us the equation: \[ 4a + 2.5s = 2820 \]

2. Total Tickets Equation: The total number of tickets sold (both adult and student) is 900. This gives us another equation: \[ a + s = 900 \]

Summary of the equations:

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

Solving the equations:

From the second equation, you can express \(a\) in terms of \(s\): \[ a = 900 - s \]

Now substitute \(a\) into the first equation: \[ 4(900 - s) + 2.5s = 2820 \] Distributing: \[ 3600 - 4s + 2.5s = 2820 \] Combining like terms: \[ 3600 - 1.5s = 2820 \] Subtracting 3600 from both sides: \[ -1.5s = 2820 - 3600 \] \[ -1.5s = -780 \] Dividing by -1.5: \[ s = \frac{-780}{-1.5} = 520 \]

Now substituting \(s = 520\) back into the equation for \(a\): \[ a + 520 = 900 \implies a = 900 - 520 = 380 \]

Final Result:

• Adult tickets sold (a): 380
• Student tickets sold (s): 520