georgia connections academy is selling tickets to its spring fling. adult tickets cost 4$ and tickets cost $2.50 the school makes @2,820 and sells 900 tickets. how many adult tickets and student tickets were sold.
Let's represent the number of adult tickets sold as a and the number of student tickets sold as s.
From the information given, we have two equations:
a + s = 900 (1) (since the total number of tickets sold is 900)
4a + 2.5s = 2820 (2) (since the total revenue from selling adult and student tickets is $2820)
To solve this system of equations, we can use the substitution method.
Rearrange equation (1):
s = 900 - a
Substitute this expression for s in equation (2):
4a + 2.5(900 - a) = 2820
Distribute 2.5:
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
Substitute this value for a in equation (1):
380 + s = 900
Subtract 380 from both sides:
s = 520
So, 380 adult tickets and 520 student tickets were sold at the spring fling.
Let's solve this step-by-step:
Let's assume the number of adult tickets sold is "x" and the number of student tickets sold is "y".
Step 1: Write the equations based on the given information:
x + y = 900 (total tickets sold)
4x + 2.5y = 2820 (total revenue generated)
Step 2: Simplify the equations if needed:
Multiply the first equation by 2.5 to eliminate the decimals:
2.5x + 2.5y = 2250
Step 3: Solve the system of equations:
Now we have the following system of equations:
2.5x + 2.5y = 2250
4x + 2.5y = 2820
Subtract the first equation from the second equation:
(4x + 2.5y) - (2.5x + 2.5y) = 2820 - 2250
1.5x = 570
Step 4: Solve for x:
Divide both sides of the equation by 1.5:
x = 570 / 1.5
x = 380
Step 5: Substitute the value of x back into one of the original equations:
380 + y = 900
y = 900 - 380
y = 520
So, 380 adult tickets and 520 student tickets were sold.
To solve this problem, we can set up a system of equations with two unknowns, representing the number of adult tickets and student tickets sold.
Let's say 'x' represents the number of adult tickets sold, and 'y' represents the number of student tickets sold.
Given that the school made a total of $2,820 from selling 900 tickets, we can create the first equation:
4x + 2.5y = 2820
We also know that the total number of tickets sold is 900, so the second equation would be:
x + y = 900
Now we have a system of two equations:
4x + 2.5y = 2820
x + y = 900
There are different methods to solve this system of equations, but I will use the substitution method here.
Rearrange the second equation to solve for x:
x = 900 - y
Now substitute this value of x into the first equation:
4(900 - y) + 2.5y = 2820
Simplify the equation:
3600 - 4y + 2.5y = 2820
-4y + 2.5y = 2820 - 3600
-1.5y = -780
y = -780 / -1.5
y = 520
Now substitute the value of y back into the second equation to find x:
x + 520 = 900
x = 900 - 520
x = 380
Therefore, the school sold 380 adult tickets and 520 student tickets for the spring fling.