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.
a +
s=
.
900 tickets are sold for the spring fling. Write an equation to represent this situation.
a+
=
Use the above systems of equations to determine how many adult and student tickets were sold.
Adult tickets:
student tickets:
Equation 1: 4a + 2.5s = 2820
Equation 2: a + s = 900
To solve for a and s, we can use substitution or elimination method. Let's use elimination here.
Multiplying Equation 2 by -4 to eliminate a:
-4a - 4s = -3600
Adding this to Equation 1:
-1.5s = -780
Solving for s:
s = 520
Substituting s back into Equation 2:
a + 520 = 900
Solving for a:
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
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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.
a +
s=
.
900 tickets are sold for the spring fling. Write an equation to represent this situation.
a+
=
Use the above systems of equations to determine how many adult and student tickets were sold.
Adult tickets:
student tickets:
I apologize for the confusion, and I will provide a corrected response below.
1. Let a be the number of adult tickets sold and s be the number of student tickets sold. The total revenue earned by selling adult and student tickets can be calculated as:
Total revenue = (4a) + (2.5s)
Since the total revenue earned by the school for selling tickets is $2,820, we can write:
4a + 2.5s = 2820
This is the equation that represents the situation to find the cost of all adult and student tickets sold.
2. Let a be the number of adult tickets sold. Since a total of 900 tickets are sold, we can write:
a + s = 900
This is the equation that represents the situation where 900 tickets are sold for the Spring Fling.
3. Now we have two equations with two variables a and s. We can use different methods to solve for a and s, such as substitution or elimination. Here, we will use the substitution method.
From Equation 2, we can write:
a = 900 - s
Substituting this value of a in Equation 1, we get:
4(900 - s) + 2.5s = 2820
Simplifying the equation, we get:
3600 - 1.5s = 2820
Subtracting 3600 from both sides, we get:
-1.5s = -780
Therefore, we get:
s = 520
Substituting the value of s in Equation 2, we get:
a + 520 = 900
Solving for a, we get:
a = 380
Therefore, the number of adult tickets sold is 380, and the number of student tickets sold is 520.