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. (7 points)
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
The equation that represents the cost of all adult and student tickets sold is:
4a + 2.5s = 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 need to solve this system of equations.
To solve the system of equations, we can use substitution or elimination method.
Using substitution method:
a + s = 900
s = 900 - a
We can substitute this value of s in the first equation:
4a + 2.5(900 - a) = 2820
Now we can solve for a:
4a + 2250 - 2.5a = 2820
1.5a + 2250 = 2820
1.5a = 570
a = 380
Substituting this value of a back into the equation a + s = 900:
380 + s = 900
s = 900 - 380
s = 520
So, 380 adult tickets and 520 student tickets were sold.
To write an equation that represents the cost of all adult and student tickets sold, we need to consider the number of adult tickets sold and the number of student tickets sold.
Since adult tickets cost $4 each and student tickets cost $2.50 each, the equation for the cost of all adult and student tickets sold would be:
4a + 2.50s = 2820
Here, "a" represents the number of adult tickets sold and "s" represents the number of student tickets sold.
To represent the number of tickets sold, we can use the information given that 900 tickets were sold. Thus, the equation for the number of tickets sold would be:
a + s = 900
Now, we can solve the system of equations to find the number of adult and student tickets sold.
To solve the system of equations, we can use substitution or elimination.
Using the substitution method, we can solve for "a" in terms of "s" in the second equation and substitute it into the first equation.
From the second equation, we have:
a = 900 - s
Substituting this into the first equation, we get:
4(900 - s) + 2.50s = 2820
Expanding and simplifying, we get:
3600 - 4s + 2.50s = 2820
Combine like terms:
-1.5s = -780
Divide both sides by -1.5:
s = 520
Substituting this value back into the second equation, we find:
a + 520 = 900
Subtract 520 from both sides:
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
To write the equation that represents the situation, we need to consider two aspects: the cost of adult tickets and the cost of student tickets.
1. The cost of adult tickets can be expressed as: $4 x a (since each adult ticket costs $4).
2. The cost of student tickets can be expressed as: $2.50 x s (since each student ticket costs $2.50).
Since the total earnings from ticket sales is given as $2,820, we can write the equation as follows:
4a + 2.50s = 2,820
Now, let's move on to the next part.
Since we know that there were a total of 900 tickets sold, we can write the equation based on the number of tickets sold:
a + s = 900
Finally, we can solve this system of equations to determine the number of adult and student tickets sold.
To find the numbers, we can use any method of solving systems of equations, such as substitution or elimination.
Let's use the substitution method:
From the second equation, we can express a in terms of s:
a = 900 - s
Now substitute this value of a in the first equation:
4(900 - s) + 2.50s = 2,820
Expanding the equation, we get:
3600 - 4s + 2.50s = 2,820
Combine like terms:
-1.50s = 2820 - 3600
-1.50s = -780
Divide both sides by -1.50 to solve for s:
s = -780 / (-1.50)
s = 520
Now substitute this value of s into the second equation to find a:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.