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.

Answer 1

To represent the situation, we can set up an equation based on the total revenue generated from selling adult and student tickets.

Let:

• $a$ = number of adult tickets sold
• $s$ = number of student tickets sold

The cost for each adult ticket is $4, and the cost for each student ticket is $2.50. The total revenue from all tickets sold is $2,820.

The equation representing this situation is:

$$4a+2.5s=2820$$

This equation can be used to find the number of adult and student tickets sold.

Answer 2

so how many adult and student tickets were sold

Answer 3

To determine the number of adult and student tickets sold, we need an additional piece of information, such as the total number of tickets sold or a specific relationship between the numbers of adult and student tickets.

However, if we only have the equation $4a+2.5s=2820$, we can express one variable in terms of another, but we cannot find unique values for $a$ and $s$ without additional information.

For example, if we wanted to express the number of student tickets in terms of the number of adult tickets, we could rearrange the equation:

$$2.5s=2820-4a$$

$$s=\frac{2820-4a}{2.5}$$

This means you can choose a specific value for $a$ (the number of adult tickets) and calculate the corresponding value for $s$ (the number of student tickets).

If you have more information (like the total number of tickets sold), please provide it, and I can help calculate the specific numbers for $a$ and $s$.

Answer 4

900 tickets were sold

Answer 5

Great! Now we have two equations to work with:

1. The revenue equation: $$4a+2.5s=2820$$

2. The total tickets sold equation: $$a+s=900$$

Now we can solve this system of equations.

First, we can express $s$ in terms of $a$ from the second equation:

$$s=900-a$$

Next, we substitute this expression for $s$ into the revenue equation:

$$4a+2.5(900-a)=2820$$

Now, distribute $2.5$:

$$4a+2250-2.5a=2820$$

Combine like terms:

$$(4-2.5)a+2250=2820$$

$$1.5a+2250=2820$$

Now, isolate $a$:

$$1.5a=2820-2250$$

$$1.5a=570$$

Now, divide by 1.5:

$$a=\frac{570}{1.5}=380$$

Now that we have $a$, we can find $s$:

$$s=900-a=900-380=520$$

So, the final numbers of tickets sold are:

• Adult tickets sold ($a$): 380
• Student tickets sold ($s$): 520