For a Saturday matinee, adult tickets cost $6.50 and kids under 12 pay only $4.00. If 90 tickets are sold for a total of $460, how many of the tickets were adult tickets and how many were sold to kids under 12?
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Let's assume the number of adult tickets sold is A and the number of kids' tickets sold is K.
The price of an adult ticket is $6.50, so the total cost of adult tickets is 6.50A.
The price of a kids' ticket is $4.00, so the total cost of kids' tickets is 4.00K.
We know that the total number of tickets sold is 90, so we can write the equation A + K = 90.
We also know that the total amount collected from ticket sales is $460, so we can write the equation 6.50A + 4.00K = 460.
Now we can solve these equations to find the values of A and K.
We can start by multiplying the first equation by 4.00 to eliminate K:
4.00A + 4.00K = 360
Now we can subtract this equation from the second equation:
6.50A + 4.00K - (4.00A + 4.00K) = 460 - 360
2.50A = 100
Dividing both sides of the equation by 2.50, we get:
A = 40
Substituting this value back into the first equation, we find:
40 + K = 90
K = 90 - 40
K = 50
Therefore, 40 adult tickets and 50 kids' tickets were sold.
To solve this problem, we can use a system of equations.
Let's assume the number of adult tickets sold is "A" and the number of kids' tickets sold is "K".
Given that the total number of tickets sold is 90, we can write the equation:
A + K = 90
The total amount collected from adult tickets would be the product of the number of adult tickets and the ticket price, which is 6.50:
6.50A
Similarly, the total amount collected from kids' tickets would be the product of the number of kids' tickets and the ticket price, which is $4.00:
4.00K
The sum of these two ticket sales should equal the total revenue of $460:
6.50A + 4.00K = 460
Now we have a system of equations:
A + K = 90
6.50A + 4.00K = 460
We can now solve this system of equations using substitution or elimination. Let's use the elimination method:
Multiply the first equation by 4 to make the coefficients of "K" the same:
4A + 4K = 360
Now subtract this equation from the second equation to eliminate "K":
(6.50A + 4.00K) - (4A + 4K) = 460 - 360
2.50A = 100
Divide both sides of the equation by 2.50 to solve for "A":
A = 100 / 2.50
A = 40
Now substitute the value of "A" into the first equation to solve for "K":
40 + K = 90
K = 90 - 40
K = 50
Therefore, 40 adult tickets and 50 kids' tickets were sold.