for the school play, 1 adult ticket cost $5 and 1 student ticket cost $3. twice as amny student tickets as adult tickets were sold. the total reciepts were $1650. how many of each kind of tickets were sold?
Adult tickets ---> x
student tickets --> 2x
5x + 3(2x) = 1650
solve
oh okay, thanks :)
To solve this problem, we can use a system of linear equations. Let's define our variables:
- Let x be the number of adult tickets sold.
- Let y be the number of student tickets sold.
According to the problem, we know that:
1) The cost of an adult ticket is $5, so the revenue from adult tickets is 5x dollars.
2) The cost of a student ticket is $3, so the revenue from student tickets is 3y dollars.
3) Twice as many student tickets were sold as adult tickets, so y = 2x.
We are also given that the total receipts were $1650, so the sum of the revenue from adult and student tickets is equal to $1650:
5x + 3y = 1650
Now, we can substitute the value of y from equation 3) into equation 5x + 3y = 1650:
5x + 3(2x) = 1650
5x + 6x = 1650
11x = 1650
x = 150
Substituting x = 150 into equation 3), we can find y:
y = 2x
y = 2(150)
y = 300
Therefore, 150 adult tickets and 300 student tickets were sold for the school play.