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.
5 answers
To represent the situation, we can set up an equation based on the total revenue generated from selling adult and student tickets.
Let:
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.
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 \( s \).
Great! Now we have two equations to work with:
The revenue equation: \[ 4a + 2.5s = 2820 \]
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:
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