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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.

adult tickets and student tickets were sold.

Options for the blanks, 510, 6.5, 2.50, s, 2820, 390, 900, 309, 591, 4, a

1 answer

To create the equations representing the situation for Georgia Connections Academy's Spring Fling tickets, we have the following information:

  1. Adult tickets cost $4 and student tickets cost $2.50.
  2. The total revenue from ticket sales is $2,820.
  3. The total number of tickets sold is 900.

Let’s break it down step by step.

Step 1: Write the Equation for Revenue

The revenue from adult tickets and student tickets sold can be expressed using the equation:

\[ 4a + 2.5s = 2820 \]

Step 2: Write the Equation for Total Tickets Sold

The total number of tickets sold can be expressed using the equation:

\[ a + s = 900 \]

Blanks Filling

Using the information above, we can fill in the response areas as follows:

  1. For the revenue equation (\(4a + 2.5s = 2820\)):

    • Fill in the first response area with 4, the second response with 2.50, and the last response area with 2820.

  2. For the total tickets sold (\(a + s = 900\)):

    • Fill in the first response area with s and the second response area with 900.

Final Answer

Now, substituting values, we summarize the filled equations:

  1. Revenue: \[ 4a + 2.50s = 2820 \]

  2. Total Tickets: \[ a + s = 900 \]

Solving the System of Equations

To find the number of adult \(a\) and student \(s\) tickets sold, we can solve this system of equations.

From the total tickets equation (\(a + s = 900\)), we can express \(s\) in terms of \(a\): \[ s = 900 - a \]

Substituting this into the revenue equation: \[ 4a + 2.50(900 - a) = 2820 \] \[ 4a + 2250 - 2.5a = 2820 \] \[ 1.5a + 2250 = 2820 \] \[ 1.5a = 570 \] \[ a = \frac{570}{1.5} = 380 \]

Using \(a = 380\) in the total tickets equation: \[ s = 900 - 380 = 520 \]

Conclusion

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

So the final answer is:

  • Adult tickets: 380
  • Student tickets: 520