A school is selling tickets to its spring fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. How many tickets were sold to adults and students seperetly.
Let's assume the number of adult tickets sold is "a" and the number of student tickets sold is "s."
Given that the adult tickets cost $4 and the student tickets cost $2.50, we can set up the following equations:
4a + 2.5s = 2820 (equation 1)
We also know that the school sold a total of "a" adult tickets and "s" student tickets, so:
a + s = Total number of tickets sold (equation 2)
We want to find the values of "a" and "s."
To solve this system of equations, we can use substitution or elimination.
Let's use the substitution method:
From equation 2, we have a = Total number of tickets sold - s.
Substituting this into equation 1, we get:
4(Total number of tickets sold - s) + 2.5s = 2820
Expanding and rearranging the equation:
4Total number of tickets sold - 4s + 2.5s = 2820
4Total number of tickets sold - 1.5s = 2820
4Total number of tickets sold = 2820 + 1.5s
Total number of tickets sold = (2820 + 1.5s)/4 (equation 3)
Now we can solve for "s":
Substituting equation 3 into equation 2, we have:
(2820 + 1.5s)/4 + s = Total number of tickets sold
Multiplying both sides of the equation by 4 to eliminate the denominator:
2820 + 1.5s + 4s = 4(Total number of tickets sold)
2820 + 5.5s = 4Total number of tickets sold
5.5s = 4Total number of tickets sold - 2820
s = (4Total number of tickets sold - 2820)/5.5 (equation 4)
We can now substitute the value of "s" from equation 4 into equation 2 to find "a":
a + (4Total number of tickets sold - 2820)/5.5 = Total number of tickets sold
Multiply both sides of the equation by 5.5 to eliminate the denominator:
5.5a + 4Total number of tickets sold - 2820 = 5.5Total number of tickets sold
5.5a - 5.5Total number of tickets sold = 2820 - 4Total number of tickets sold
-0.5Total number of tickets sold = 2820
Total number of tickets sold = 2820 / -0.5
Total number of tickets sold = -5640
Something seems off in the calculations. The number of tickets sold should be positive, so there might be an error in the given information or equations. Is there any additional information you can provide?
A school is selling tickets to its spring fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. How many tickets were sold to adults and how many were sold to students.
Let's assume the number of adult tickets sold is "a" and the number of student tickets sold is "s."
Given that the adult tickets cost $4 and the student tickets cost $2.50, we can set up the following equations:
4a + 2.5s = 2820 (equation 1) - representing the total revenue from ticket sales.
We also know that the total number of tickets sold is the sum of adult and student tickets:
a + s = Total number of tickets sold (equation 2)
We want to find the values of "a" and "s" that satisfy these equations.
To solve this system of equations, we can use substitution or elimination.
Let's use the substitution method:
From equation 2, we have a = Total number of tickets sold - s.
Substituting this into equation 1, we get:
4(Total number of tickets sold - s) + 2.5s = 2820
Expanding and rearranging the equation:
4Total number of tickets sold - 4s + 2.5s = 2820
4Total number of tickets sold - 1.5s = 2820
4Total number of tickets sold = 2820 + 1.5s
Total number of tickets sold = (2820 + 1.5s)/4 (equation 3)
Now we can solve for "s":
Substituting equation 3 into equation 2, we have:
(2820 + 1.5s)/4 + s = Total number of tickets sold
Multiplying both sides of the equation by 4 to eliminate the denominator:
2820 + 1.5s + 4s = 4(Total number of tickets sold)
2820 + 5.5s = 4Total number of tickets sold
5.5s = 4Total number of tickets sold - 2820
s = (4Total number of tickets sold - 2820)/5.5 (equation 4)
We can now substitute the value of "s" from equation 4 into equation 2 to find "a":
a + (4Total number of tickets sold - 2820)/5.5 = Total number of tickets sold
Multiply both sides of the equation by 5.5 to eliminate the denominator:
5.5a + 4Total number of tickets sold - 2820 = 5.5Total number of tickets sold
5.5a - 5.5Total number of tickets sold = 2820 - 4Total number of tickets sold
-0.5Total number of tickets sold = 2820
Total number of tickets sold = 2820 / -0.5
Total number of tickets sold = -5640
Uh-oh, there seems to be an error in the calculations. The number of tickets sold cannot be negative. Let's assume there was a typo in the question. Instead of the school making $2,820, let's assume they made $2,820 from adult and student ticket sales combined.
Let's try solving it again:
Equation 1: 4a + 2.5s = 2820
Equation 2: a + s = Total number of tickets sold
To eliminate the variable "a" from equation 2, we can solve equation 2 for "a":
a = Total number of tickets sold - s
Substituting this into equation 1, we have:
4(Total number of tickets sold - s) + 2.5s = 2820
4Total number of tickets sold - 4s + 2.5s = 2820
4Total number of tickets sold - 1.5s = 2820
Rearranging the equation:
-1.5s = 2820 - 4Total number of tickets sold
1.5s = 4Total number of tickets sold - 2820
s = (4Total number of tickets sold - 2820)/1.5
Now, we can substitute the value of "s" into equation 2 to find "a":
a + s = Total number of tickets sold
a + (4Total number of tickets sold - 2820)/1.5 = Total number of tickets sold
Multiplying both sides by 1.5 to eliminate the denominator:
1.5a + 4Total number of tickets sold - 2820 = 1.5Total number of tickets sold
1.5a - 1.5Total number of tickets sold = 2820 - 4Total number of tickets sold
-0.5Total number of tickets sold = -2.5Total number of tickets sold + 2820
2Total number of tickets sold = 2820
Total number of tickets sold = 2820 / 2
Total number of tickets sold = 1410
Now, substituting this value of "Total number of tickets sold" into equation 2:
a + 1410 = 1410
a = 0
Therefore, 0 adult tickets were sold, and 1410 student tickets were 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.
To find the cost of all adult and student tickets sold, we can set up the following equation:
Cost of adult tickets + Cost of student tickets = Total cost
The cost of adult tickets can be calculated by multiplying the number of adult tickets sold (represented by "a") by the cost of each adult ticket ($4). Similarly, the cost of student tickets can be calculated by multiplying the number of student tickets sold (represented by "s") by the cost of each student ticket ($2.50).
Therefore, the equation is:
4a + 2.50s = Total cost
In this equation, "a" represents the number of adult tickets sold, "s" represents the number of student tickets sold, and "Total cost" represents the total cost of all adult and student tickets sold.
900 tickets are sold for the spring fling. write an equation to represent the situation.
To represent the situation where 900 tickets are sold for the spring fling, we can set up the following equation:
Total number of adult tickets + Total number of student tickets = 900
In this case, we do not have specific information about the number of adult or student tickets sold. So, let's use "a" to represent the number of adult tickets sold and "s" to represent the number of student tickets sold.
The equation is:
a + s = 900
In this equation, "a" represents the number of adult tickets sold, "s" represents the number of student tickets sold, and the sum of the two represents the total number of tickets sold, which is given as 900.
Use the other systems of equations to determine how many adult and student tickets were sold.
Let's use the system of equations from the previous response to determine the number of adult and student tickets sold:
Equation 1: 4a + 2.50s = Total cost
Equation 2: a + s = 900
We have two equations with two variables. We can solve this system of equations using either substitution or elimination method.
Using substitution method:
From Equation 2, we have a = 900 - s.
Substituting this into Equation 1:
4(900 - s) + 2.50s = Total cost
3600 - 4s + 2.50s = Total cost
3600 - 1.50s = Total cost
Now, let's substitute a value for "Total cost" to solve for "s."
Let's assume the Total cost is $2820, as mentioned previously.
3600 - 1.50s = 2820
Now, let's solve for "s":
-1.50s = 2820 - 3600
-1.50s = -780
s = (-780) / (-1.50)
s = 520
Now, substitute the value of "s" into Equation 2 to solve for "a":
a + s = 900
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold for the spring fling.
To solve this problem, we need to set up a system of equations. Let's represent the number of adult tickets sold as "A" and the number of student tickets sold as "S".
Based on the information given, we can set up the following equations:
Equation 1: A + S = total number of tickets sold
Equation 2: 4A + 2.50S = 2,820 (since the total amount earned is $2,820)
Now we have a system of two equations with two variables:
Equation 1: A + S = ?
Equation 2: 4A + 2.50S = 2820
There are different ways to solve this system of equations. Let's use the substitution method:
From Equation 1, we can rewrite it as A = (total number of tickets sold) - S.
Now we can substitute this value of A into Equation 2:
4((total number of tickets sold) - S) + 2.50S = 2820
Expanding this equation:
4(total number of tickets sold) - 4S + 2.50S = 2820
Combine like terms:
4(total number of tickets sold) - 1.50S = 2820
Next, we need to isolate the S variable:
-1.50S = 2820 - 4(total number of tickets sold)
Divide both sides by -1.50:
S = (2820 - 4(total number of tickets sold))/(-1.50)
Now we know the value of S, we can substitute it back into Equation 1 to find A:
A + S = total number of tickets sold
A + ((2820 - 4(total number of tickets sold))/(-1.50)) = total number of tickets sold
Simplify and rearrange the equation to solve for A:
(A * -1.50) + (2820 - 4(total number of tickets sold))/(-1.50) = total number of tickets sold
(-1.50A - 2820 + 4(total number of tickets sold))/(-1.50) = total number of tickets sold
-1.50A - 2820 + 4(total number of tickets sold) = (-1.50)(total number of tickets sold)
-1.50A - 2820 + 4(total number of tickets sold) = -1.50(total number of tickets sold)
Now we can simplify and bring all terms with A to one side of the equation:
-1.50A - 1.50(total number of tickets sold) = 2820
-1.50A + 1.50(total number of tickets sold) = -2820
Combine like terms:
1.50(total number of tickets sold) - 1.50A = -2820
Now we can divide by 1.50 to solve for A:
A = (-2820)/(1.50 - total number of tickets sold)
Finally, substitute the number of adult tickets, A, into Equation 1 to find the number of student tickets, S:
(total number of tickets sold) - (2820/(1.50 - total number of tickets sold)) = S