Question

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) 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. a + S = 900 tickets are sold for the spring fling. Write an equation to represent this situation. a +! Use the above system of equations to determine how many adult and student tickets were sold. adult tickets and student tickets were sold. :: 390 :: 2820 :: 2.50 :: 510 :: 309 :: 4 :: 900 ":a :: 591 :: 380 :: 6.5 :: 520

Answer 1

To solve the problem, we first need to set up a system of equations based on the information provided.

Let:

• \( a \) = number of adult tickets sold
• \( s \) = number of student tickets sold

From the problem, we know two things:

1. The total revenue from ticket sales is $2,820. The adult tickets cost $4 and student tickets cost $2.50, which gives us the first equation: \[ 4a + 2.5s = 2820 \]

2. The total number of tickets sold is 900, which gives us the second equation: \[ a + s = 900 \]

Now we have the system of equations:

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

Next, we can solve this system of equations to find the values of \( a \) and \( s \).

Step 1: Solve the second equation for \( s \)

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

Step 2: Substitute \( s \) into the first equation

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

Step 3: Distribute and combine like terms

\[ 4a + 2250 - 2.5a = 2820 \]

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

Step 4: Isolate \( a \)

Subtract 2250 from both sides: \[ 1.5a = 2820 - 2250 \] \[ 1.5a = 570 \]

Now divide by 1.5: \[ a = \frac{570}{1.5} = 380 \]

Step 5: Find \( s \) using the value of \( a \)

Now substitute \( a = 380 \) back into the equation \( s = 900 - a \): \[ s = 900 - 380 = 520 \]

Conclusion

The number of adult tickets sold is \( 380 \) and the number of student tickets sold is \( 520 \). Thus, the solution to the problem is:

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