A movie theatre sells two types of tickets: adult and child. On Tuesday, the theatre sold 100 adult tickets and 70 child tickets and made a total of $1,100. On Wednesday, the theatre sold 50 adult tickets and 50 child tickets and made a total of $625. How much is an adult movie theatre ticket?
100A + 70C = 1100
50A + 50C = 625
Divide first equation by 2.
50A + 35C = 550
Subtract that from the second equation.
15C = 75
Solve for C, then insert into any of above equations to find A.
To find the price of an adult movie ticket, we can set up a system of equations based on the given information.
Let's assume the price of an adult ticket is "x" dollars.
From the given information on Tuesday:
The theatre sold 100 adult tickets, which would amount to 100x dollars.
The theatre also sold 70 child tickets, but we don't need this information to find the price of an adult ticket.
The total earnings on Tuesday were $1,100.
So, our equation for Tuesday would be: 100x + (70 * child ticket price) = $1,100.
From the given information on Wednesday:
The theatre sold 50 adult tickets, which would amount to 50x dollars.
The theatre also sold 50 child tickets, but we don't need this information to find the price of an adult ticket.
The total earnings on Wednesday were $625.
So, our equation for Wednesday would be: 50x + (50 * child ticket price) = $625.
Since we only want to find the price of an adult ticket, we can ignore the child ticket price in both equations.
Simplifying the equations, we get:
100x = $1,100 and 50x = $625.
Now, let's solve for "x."
Dividing both sides of the first equation by 100:
x = $1,100 / 100
x = $11
Dividing both sides of the second equation by 50:
x = $625 / 50
x = $12.50
Since these equations represent different scenarios (Tuesday and Wednesday), we need to verify which one is correct.
Using the price of $11 for an adult ticket:
100 * $11 + 70 * child ticket price = $1,100
$1,100 + 70 * child ticket price = $1,100
We can see that the equation doesn't hold true, so we can conclude that $11 is not the correct price for an adult ticket.
Using the price of $12.50 for an adult ticket:
50 * $12.50 + 50 * child ticket price = $625
$625 + 50 * child ticket price = $625
This equation holds true, so we can conclude that the correct price for an adult movie theatre ticket is $12.50.
To find the price of an adult movie theatre ticket, we can set up a system of equations based on the given information.
Let's represent the price of an adult ticket as "x" and the price of a child ticket as "y".
Based on the information given on Tuesday:
- The theatre sold 100 adult tickets at a price of "x" each, for a total of 100x dollars.
- The theatre sold 70 child tickets at a price of "y" each, for a total of 70y dollars.
- The total revenue generated on Tuesday was $1,100.
So, our first equation can be written as:
100x + 70y = 1,100
Similarly, based on the information given on Wednesday:
- The theatre sold 50 adult tickets at a price of "x" each, for a total of 50x dollars.
- The theatre sold 50 child tickets at a price of "y" each, for a total of 50y dollars.
- The total revenue generated on Wednesday was $625.
So, our second equation can be written as:
50x + 50y = 625
Now we can solve this system of equations to find the value of "x", which represents the price of an adult movie theatre ticket.
We will use the method of elimination to solve the system.
First, let's multiply the first equation by 5 and the second equation by 2 to make the coefficients of "y" equal and eliminate "y" when the two equations are added together:
(5) * (100x + 70y) = (5) * (1,100)
(2) * (50x + 50y) = (2) * (625)
This simplifies the equations to:
500x + 350y = 5,500
100x + 100y = 1,250
Now, let's subtract the second equation from the first equation:
(500x + 350y) - (100x + 100y) = 5,500 - 1,250
Simplifying further:
400x + 250y = 4,250
Now, we have a new equation:
400x + 250y = 4,250
To eliminate "y" from this equation, let's divide both sides by 250:
(400x + 250y) / 250 = 4,250 / 250
Simplifying further:
1.6x + y = 17
Now, we have a linear equation in one variable. To solve for "x", we need to isolate it. Let's subtract "y" from both sides:
1.6x + y - y = 17 - y
Simplifying further:
1.6x = 17 - y
Finally, we can substitute the value of "y" from the second equation into this equation:
1.6x = 17 - (100x + 100y) / 100
Simplifying further:
1.6x = 17 - x - y
Since we are looking for the price of an adult ticket (represented by "x"), we need to substitute the value of "y" from the first equation:
1.6x = 17 - x - (1,100 - 100x) / 100
Simplifying further:
1.6x = 17 - x - 11 + x / 100
Combining like terms:
1.6x = 6 - x / 100
Multiplying both sides by 100 to get rid of the fraction:
160x = 600 - x
Adding "x" to both sides:
160x + x = 600
Simplifying further:
161x = 600
Dividing both sides by 161 to solve for "x":
x = 600 / 161
Calculating the value of "x":
x ≈ 3.727
Approximately, the price of an adult movie theatre ticket is $3.73.