Georgia connections academy is selling tickets to its spring fling. Adults 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 variables s for student tickets and a for adult tickets sold.
Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variables s for student tickets and a for adults tickets sold. 900 tickets are sold for the spring fling. Write an equation to represent this situation. Use the above system of equations to determine how many adult and student tickets were sold.
From the problem, we can create two equations based on the given information:
1. The cost equation: 4a + 2.5s = 2820
(Where a is the number of adult tickets sold and s is the number of student tickets sold)
2. The quantity equation: a + s = 900
(Where a + s represents the total number of tickets sold)
To determine the number of adult and student tickets sold, we can solve this system of equations.
Use the above system of equations to determine how many adult and student tickets were sold
To determine how many adult and student tickets were sold, we can solve the system of equations:
1. 4a + 2.5s = 2820
2. a + s = 900
We can solve this system using substitution or elimination. Let's use the substitution method.
From equation 2, we can express a in terms of s: a = 900 - s.
Substituting this value of a in equation 1:
4(900 - s) + 2.5s = 2820
3600 - 4s + 2.5s = 2820
-1.5s = -780
s = -780 / -1.5
s = 520
Substituting s = 520 in equation 2 to find the value of a:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
To represent the cost of all adult and student tickets sold, we can use the following equation:
Equation 1:
4a + 2.50s = 2,820
This equation represents the total revenue made by selling adult and student tickets.
Since 900 tickets are sold for the spring fling, we can write another equation to represent this situation:
Equation 2:
a + s = 900
Now, let's use this system of equations to determine how many adult and student tickets were sold.
We can solve this system of equations by substitution or elimination method. Let's solve it using substitution.
First, solve Equation 2 for a in terms of s:
a = 900 - s
Substitute this value of a in Equation 1:
4(900 - s) + 2.50s = 2,820
Now, simplify and solve for s:
3,600 - 4s + 2.50s = 2,820
Combine similar terms:
-1.50s + 3,600 = 2,820
Subtract 3,600 from both sides:
-1.50s = 2,820 - 3,600
-1.50s = -780
Divide both sides by -1.50:
s = -780 / -1.50
s ≈ 520
Now that we have the value of s, we can substitute it back into Equation 2 to find the value of a:
a + 520 = 900
Subtract 520 from both sides:
a = 900 - 520
a ≈ 380
Therefore, approximately 380 adult tickets and 520 student tickets were sold.