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.

Question

(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.

Answer 1

To write the equations representing the situation for the Spring Fling tickets, we need to keep in mind two separate aspects: the total revenue generated from ticket sales and the total number of tickets sold.

1. Total Revenue Equation:
   Adult tickets cost $4 and student tickets cost $2.50, and the total revenue is $2,820. The equation can be written as: \[ 4a + 2.5s = 2820 \]

2. Total Tickets Sold Equation:
   The total number of tickets sold is 900. This equation can be represented as: \[ a + s = 900 \]

Now, we have the following system of equations:

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

To determine how many adult (a) and student (s) tickets were sold, we'll use the second equation to express one variable in terms of the other. From the second equation: \[ s = 900 - a \]

Now, substitute this expression for \(s\) into the first equation: \[ 4a + 2.5(900 - a) = 2820 \]

Now, distribute the \(2.5\): \[ 4a + 2250 - 2.5a = 2820 \]

Combine like terms: \[ (4a - 2.5a) + 2250 = 2820 \] \[ 1.5a + 2250 = 2820 \]

Now, isolate \(a\): \[ 1.5a = 2820 - 2250 \] \[ 1.5a = 570 \] \[ a = \frac{570}{1.5} \] \[ a = 380 \]

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

Summary

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

So the complete system of equations was used effectively to find the number of adult and student tickets sold.