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.

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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.

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Answer 1

To represent the situation involving ticket sales at Georgia Connections Academy, we can set up the following equations.

1. Equation for total revenue from ticket sales: Since adult tickets cost $4 and student tickets cost $2.50, and the total revenue is $2,820, the equation will be:

   \[ 4a + 2.5s = 2820 \]

2. Equation for the total number of tickets sold: If 900 tickets were sold in total, the equation will be:

   \[ a + s = 900 \]

Now we can summarize the responses for each equation.

• For the revenue equation:
  \[ 4a + 2.5s = 2820 \]

• For the total number of tickets equation:
  \[ a + s = 900 \]

Next, you can solve this system of equations to find the number of adult tickets (a) and student tickets (s) sold.

To do this, we can use substitution or elimination. Here, we can use substitution:

From the second equation, solve for one variable: \[ s = 900 - a \]

Now substitute \(s\) into the first equation: \[ 4a + 2.5(900 - a) = 2820 \] Distribute: \[ 4a + 2250 - 2.5a = 2820 \] Combine like terms: \[ 1.5a + 2250 = 2820 \] Subtract 2250 from both sides: \[ 1.5a = 570 \] Divide by 1.5: \[ a = 380 \]

Now use this value to find \(s\): \[ s = 900 - a = 900 - 380 = 520 \]

So, the final answers are:

• 380 adult tickets and 520 student tickets were sold.