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 variables 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 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 system of equations to determine how many adult and student tickets were sold.
_ adult tickets and _ student tickets were sold.
Word bank:
309
2.50
2820
S
4
900
520
a
390
6.5
380
591
510
The equation that represents the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
The equation that represents the number of tickets sold is:
a + s = 900
To determine how many adult and student tickets were sold, we can solve this system of equations.
One way to solve this system of equations is by substitution. We can solve the second equation for a and substitute it into the first equation:
a = 900 - s
Substituting this into the first equation:
4(900 - s) + 2.50s = 2820
Distributing and combining like terms:
3600 - 4s + 2.50s = 2820
3600 - 1.50s = 2820
Subtracting 3600 from both sides:
-1.50s = -780
Dividing by -1.50:
s = 520
Substituting this back into the second equation:
a + 520 = 900
Subtracting 520 from both sides:
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
To find the cost of all adult and student tickets sold, we can set up the following equation:
4a + 2.50s = 2820
To represent the number of total tickets sold, we can set up another equation:
a + s = 900
Now we can solve this system of equations to determine how many adult and student tickets were sold.
Using the substitution method, we can solve for a in terms of s in the second equation:
a = 900 - s
Substituting this value of a into the first equation, we get:
4(900 - s) + 2.50s = 2820
Expanding and simplifying this equation, we have:
3600 - 4s + 2.50s = 2820
-1.5s = 2820 - 3600
-1.5s = -780
Dividing both sides by -1.5, we get:
s = (-780) / (-1.5)
s ≈ 520
Substituting this value of s back into the second equation, we can solve for a:
a + 520 = 900
a ≈ 900 - 520
a ≈ 380
Therefore, 380 adult tickets and 520 student tickets were sold.
To find the equation that represents the cost of all adult and student tickets sold, we can use the given information on ticket prices and the total revenue made by the school.
Let's define the variables:
a = number of adult tickets sold
s = number of student tickets sold
The cost of adult tickets is $4 per ticket, so the total cost of adult tickets sold is 4a.
The cost of student tickets is $2.50 per ticket, so the total cost of student tickets sold is 2.50s.
The school made $2,820 in revenue, so the equation representing this situation is:
4a + 2.50s = 2820
Now let's move on to the second part of the question.
If 900 tickets were sold for the Spring Fling, the total number of tickets sold is a + s = 900.
Using the system of equations above, we can solve for the values of a and s.
Let's substitute the equation a + s = 900 into the first equation:
4a + 2.50s = 2820
Now, we can solve for a and s using the substitution method or any other suitable method.
After calculating, we find that a = 390 and s = 510.
Therefore, 390 adult tickets and 510 student tickets were sold.