Tickets to a local movie were sold at $4.00 for adults and $2.50 for students. If 287 tickets were sold for a total of $1107.50, how many adult tickets were sold?
4 a + 2.5 s = 1107.50
a + s = 287
4 a + 4 s = 1148
4 a + 2.5 s = 1107.50
-----------------------------subtract
1.5 s = 40.5
s = 27
a = 287 - 27 = 260
To solve this problem, we can set up a system of equations using the given information.
Let's assume the number of adult tickets sold is 'A' and the number of student tickets sold is 'S'.
According to the problem, the total revenue from ticket sales is $1107.50, which can be expressed as:
4A + 2.5S = 1107.50 -- Equation (1)
Also, the total number of tickets sold is 287, so we have:
A + S = 287 -- Equation (2)
To solve this system of equations, we can use substitution or elimination. Let's use the elimination method:
Multiply Equation (2) by 2.5 to make the coefficients of S the same:
2.5A + 2.5S = 2.5 * 287
2.5A + 2.5S = 717.50 -- Equation (3)
Now, subtract Equation (3) from Equation (1) to eliminate S:
(4A + 2.5S) - (2.5A + 2.5S) = 1107.50 - 717.50
Simplifying the equation:
4A - 2.5A = 390
1.5A = 390
Divide both sides by 1.5 to isolate A:
A = 390 / 1.5
A = 260
Therefore, 260 adult tickets were sold.
Let's assume the number of adult tickets sold to be 'x' and the number of student tickets sold to be 'y'.
According to the information given, the cost of one adult ticket is $4.00 and the cost of one student ticket is $2.50.
The total number of tickets sold is 287, so we can write the equation:
x + y = 287 ...(Equation 1)
The total revenue is $1107.50. Since the revenue from each adult ticket is $4.00 and the revenue from each student ticket is $2.50, we can write the equation:
4x + 2.5y = 1107.50 ...(Equation 2)
We can solve this system of equations to find the value of x (the number of adult tickets sold).