A college sold tickets to a play at $4 per ticket. anyone who attended and purchased a ticket at the door had to pay $5 a ticket. a total of 480 people attended the play and the Revenue from ticket sales was $2,100. how many people bought tickets in advance and how many people bought tickets at the door?
number of advanced tickets ---- x
number of at door tickets ----- 480-x
4x + 5(480-x) = 2100
solve for x
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Let's assume the number of people who bought tickets in advance is 'x', and the number of people who bought tickets at the door is 'y'.
According to the information given, the total number of people who attended the play is 480, so we can write the equation:
x + y = 480
The price of each ticket bought in advance is $4, and the price of each ticket bought at the door is $5. The total revenue from ticket sales is $2,100.
The revenue from tickets bought in advance is 4x, and the revenue from tickets bought at the door is 5y. Therefore, we have the equation:
4x + 5y = 2,100
We have a system of two equations:
x + y = 480
4x + 5y = 2,100
We can solve this system of equations using substitution or elimination.
Let's use the substitution method. Rearrange the first equation to solve for 'x':
x = 480 - y
Substitute this value of 'x' into the second equation:
4(480 - y) + 5y = 2,100
1,920 - 4y + 5y = 2,100
y = 2,100 - 1,920
y = 180
Now substitute the value of 'y' back into the first equation to solve for 'x':
x + 180 = 480
x = 480 - 180
x = 300
Therefore, 300 people bought tickets in advance, and 180 people bought tickets at the door.
To find out how many people bought tickets in advance and how many bought tickets at the door, let's set up a system of equations based on the given information.
Let's assume the number of people who bought tickets in advance is 'x', and the number of people who bought tickets at the door is 'y'.
From the given information, we know the following:
1) The total number of people who attended the play is 480: x + y = 480
2) The revenue from ticket sales was $2,100: 4x + 5y = 2100
Now we can solve this system of equations to find the values of 'x' and 'y'.
To solve the system of equations above, we can use the method of substitution or elimination. Let's use the substitution method here:
From equation 1), we have x = 480 - y. Substitute this value of x into equation 2).
4(480 - y) + 5y = 2100
1920 - 4y + 5y = 2100
1920 + y = 2100
y = 2100 - 1920
y = 180
Now substitute the value of y back into equation 1) to find x:
x + 180 = 480
x = 480 - 180
x = 300
Therefore, 300 people bought tickets in advance, and 180 people bought tickets at the door.