suppose that there are two types of tickets to a show: advanced and same-day. The combined cost of one advanced and one same-day is $55. for one performance, 35 advanced tickets and 25 same-day tickets were sold. the total amount paid was $1525. what is the price of each kind of ticket?
a + s = 55
35a + 25s = 1525
substituting for s,
35a + 25(55-a) = 1525
now finish it off by solving for a, then use that to find s.
Let's suppose the price of an advanced ticket is 'x' dollars and the price of a same-day ticket is 'y' dollars.
According to the given information:
1. The combined cost of one advanced and one same-day ticket is $55.
So, we can write the equation: x + y = 55 ----(Equation 1)
2. 35 advanced tickets and 25 same-day tickets were sold, and the total amount paid was $1525.
So, we can write the equation: 35x + 25y = 1525 ----(Equation 2)
Now, we can solve the system of equations (Equation 1 and Equation 2) to find the values of 'x' and 'y'.
Let's multiply Equation 1 by 35 to eliminate 'x' and get the new equation:
35(x + y) = 35(55)
35x + 35y = 1925 ----(Equation 3)
Now, we can subtract Equation 2 from Equation 3 to eliminate 'y':
(35x + 35y) - (35x + 25y) = 1925 - 1525
10y = 400
Dividing both sides of the equation by 10, we get:
y = 40
Substituting the value of 'y' in Equation 1, we can find the value of 'x':
x + 40 = 55
x = 55 - 40
x = 15
Therefore, the price of an advanced ticket is $15 and the price of a same-day ticket is $40.
To find the price of each kind of ticket, let's assign variables to represent the unknowns. Let's say the price of an advanced ticket is "x" dollars and the price of a same-day ticket is "y" dollars.
From the problem statement, we know the following information:
1. The combined cost of one advanced and one same-day ticket is $55. Therefore, we can write an equation: x + y = 55.
2. For one performance, 35 advanced tickets and 25 same-day tickets were sold. So, the total number of advanced tickets sold is 35, and the total number of same-day tickets sold is 25.
3. The total amount paid was $1525. We can create another equation using this information. Since the number of advanced tickets sold is 35 and their price is "x" dollars, the total amount obtained from selling advanced tickets is 35x. Similarly, the total amount obtained from selling same-day tickets is 25y. Adding these amounts together should equal $1525, so we can write the equation: 35x + 25y = 1525.
We now have a system of two equations:
Equation 1: x + y = 55
Equation 2: 35x + 25y = 1525
To solve this system, we can use the method of substitution or elimination. Let's use the elimination method:
Multiply Equation 1 by 25:
25x + 25y = 1375
Subtract the above equation from Equation 2:
35x + 25y - (25x + 25y) = 1525 - 1375
10x = 150
Divide both sides by 10:
x = 15
Substitute the value of x into Equation 1:
15 + y = 55
y = 55 - 15
y = 40
Therefore, the price of an advanced ticket is $15, and the price of a same-day ticket is $40.