Suppose that there are two types of tickets to a show Advanced and same day. The combined cost of one advance ticket and one same day ticket is 55. for one performance 25 advanced tickets and 40 same day tickets were sold the total amount paid for the tickets was 1600 what was the price of each kind of ticket?
a + s = 55
25 a + 40 s = 1600
multiplying 1st equation by 25 ... 25 a + 25s = 1375
subtracting equations to eliminate a ... 15 s = 1600 - 1375
Let's assume the price of an advanced ticket is A dollars and the price of a same day ticket is S dollars.
According to the given information, we know that the combined cost of one advance ticket and one same day ticket is 55 dollars. This can be represented by the equation:
A + S = 55 [Equation 1]
We are also told that 25 advanced tickets and 40 same day tickets were sold, with a total amount paid for the tickets being 1600 dollars. This can be represented by the equation:
25A + 40S = 1600 [Equation 2]
To solve this system of equations, we can use elimination or substitution method. Let's use the substitution method here.
From Equation 1, we can isolate A in terms of S:
A = 55 - S
Now substitute this value of A in Equation 2:
25(55 - S) + 40S = 1600
Simplify the equation:
1375 - 25S + 40S = 1600
15S = 1600 - 1375
15S = 225
S = 225/15
S = 15
Now substitute the value of S back into Equation 1:
A + 15 = 55
A = 55 - 15
A = 40
So, the price of an advanced ticket is 40 dollars and the price of a same-day ticket is 15 dollars.
To find the price of each kind of ticket, let's assign variables to the unknowns. Let "x" represent the price of an advanced ticket and "y" represent the price of a same day ticket.
From the given information, we can form two equations:
Equation 1: x + y = 55 (the combined cost of one advance ticket and one same day ticket is 55)
Equation 2: 25x + 40y = 1600 (the total amount paid for the tickets was 1600)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
1. Solve Equation 1 for x:
x = 55 - y
2. Substitute the value of x in Equation 2:
25(55 - y) + 40y = 1600
3. Simplify the equation:
1375 - 25y + 40y = 1600
15y = 225
4. Solve for y:
y = 15
Now, substitute the value of y back into Equation 1 to find x:
x + 15 = 55
x = 55 - 15
x = 40
Therefore, the price of an advanced ticket is $40, and the price of a same day ticket is $15.