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 and _____
student tickets.
a + 2.5s = 2820
a + s = 900
Using substitution, we can solve for one variable in terms of the other:
a = 900 - s
Substituting into the first equation:
(900 - s) + 2.5s = 2820
1.5s = 1920
s = 1280
Substituting back into the second equation:
a + 1280 = 900
a = -380 (this doesn't make sense, since we can't have negative tickets, so there must have been an error in the problem)
To write an equation that represents the cost of all adult and student tickets sold, we can use the given information.
Let's start by assigning variables to the unknown quantities:
a = number of adult tickets sold
s = number of student tickets sold
Now let's write the equation for the cost of all adult and student tickets sold:
4a + 2.50s = 2,820
To represent the total number of tickets sold, which is 900, we can use the equation:
a + s = 900
Now, let's solve this system of equations to find the number of adult and student tickets sold.
Using the given equation 4a + 2.50s = 2,820 and substituting the value of a from the second equation:
4(900 - s) + 2.50s = 2,820
Expanding and simplifying:
3,600 - 4s + 2.50s = 2,820
-1.50s = 2,820 - 3,600
-1.50s = -780
s = -780 / -1.50
s = 520
Now substituting the value of s back into the second equation:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, the number of adult tickets sold is 380, and the number of student tickets sold is 520.
To find the equation representing the cost of all adult and student tickets sold, we need to consider the information provided:
Adult tickets cost $4, so the revenue from adult tickets sold can be represented as 4a, where a represents the number of adult tickets sold.
Student tickets cost $2.50, so the revenue from student tickets sold can be represented as 2.50s, where s represents the number of student tickets sold.
The school makes $2,820 in total, so the equation can be written as:
4a + 2.50s = 2,820.
To represent the equation for the number of tickets sold in the second situation, where 900 tickets are sold for the spring fling, we can add up the number of adult tickets sold (a) and the number of student tickets sold (s):
a + s = 900.
Now, let's solve the system of equations using substitution to determine the number of adult and student tickets sold.
First, solve the second equation for a:
a = 900 - s.
Substitute this expression for a in the first equation:
4(900 - s) + 2.50s = 2,820.
Now, solve for s:
3,600 - 4s + 2.50s = 2,820.
-1.50s = 2,820 - 3,600.
-1.50s = -780.
s = -780 / -1.50.
s = 520.
Now, substitute this value of s back into the second equation to find a:
a + 520 = 900.
a = 900 - 520.
a = 380.
Therefore, the number of adult tickets sold is 380, and the number of student tickets sold is 520.