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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

BOT PUT A ANSWER FOR EVERY "RESPONCE AREA" NOT JUST THE ALL AND ALL ANNOYING DUMMY

1 answer

Let's break down the equations step by step based on the information provided.

Step 1: Write the equation for the total revenue from ticket sales.

Adult tickets cost $4, and student tickets cost $2.50, with a total revenue of $2,820. So, the equation that combines the cost of all adult and student tickets is:

Equation 1:
\[ 4a + 2.5s = 2820 \]

Step 2: Write the equation for the total number of tickets sold.

The total number of tickets sold (adult and student) is 900. Thus, the equation representing the total number of tickets sold is:

Equation 2:
\[ a + s = 900 \]

Step 3: Fill in the Response areas.

  1. For the first equation's representation of ticket sales:
    • Response area a: 4a
    • Response area s: 2.50s
    • Response area: 2820

Putting it in the format you asked: \[ 4a + 2.50s = 2820 \]

  1. For the second equation representing total tickets sold:
    • Response area a: a
    • Response area: s
    • Response area: 900

Putting it in the format you asked: \[ a + s = 900 \]

Final Step: Solve the system of equations.

Now we can use the two equations to find the values for \( a \) (adult tickets) and \( s \) (student tickets).

Using Equation 2: \[ s = 900 - a \]

Now substitute \( s \) into Equation 1: \[ 4a + 2.5(900 - a) = 2820 \]

Expanding it gives: \[ 4a + 2250 - 2.5a = 2820 \]

Combining like terms results in: \[ 1.5a + 2250 = 2820 \]

Subtract 2250 from both sides: \[ 1.5a = 570 \]

Dividing by 1.5: \[ a = 380 \] (adult tickets sold)

Now, substitute \( a \) back to find \( s \): \[ s = 900 - 380 = 520 \] (student tickets sold)

Conclusion:

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

In summary:

  • Ticket sale equation: \( 4a + 2.50s = 2820 \)
  • Total tickets equation: \( a + s = 900 \)
  • The solution to the system is \( a = 380 \) and \( s = 520 \).