At a college function, a total of 180 tickets were sold. The tickets were priced at $5, $10, and $15, and the money collected that day was $1,900. The sum of the numbers of $5 and $15 tickets sold was twice the
number of $10 tickets sold. Find the number of each type of ticket sold for the college function.
If the quantity of tickets is x,y,x for t5,10,15 dollar tickets, respectively, then we have
x+y+z = 180
5x+10y+15z = 1900
x+z = 2y
(x,y,z) = (50,60,70)
Thank you Steve.
Thank you Steve
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns:
Let's say the number of $5 tickets sold is x.
Let's say the number of $10 tickets sold is y.
Let's say the number of $15 tickets sold is z.
We are given the following information:
1. The total number of tickets sold is 180: x + y + z = 180.
2. The total amount of money collected is $1,900: $5x + $10y + $15z = $1,900.
3. The sum of the numbers of $5 and $15 tickets sold is twice the number of $10 tickets sold: x + z = 2y.
Now we can solve this system of equations:
From equation 3, we can express x in terms of y: x = 2y - z.
Substituting x = 2y - z into equation 1, we have: 2y - z + y + z = 180.
Combining like terms, we get: 3y = 180.
Dividing both sides by 3, we find: y = 60.
Now that we know y = 60, we can substitute it into equation 3 to find x and z:
x + z = 2y
x + z = 2(60)
x + z = 120
Since the total number of tickets sold is 180 (equation 1), we can substitute the values of x and z into this equation:
x + y + z = 180
(2(60) - z) + 60 + z = 180
(120 - z) + 60 + z = 180
180 - z = 180 - 60
-z = -60
z = 60
Now substitute z = 60 back into the equation x + z = 120:
x + z = 120
x + 60 = 120
x = 60
Therefore, the number of $5 tickets sold (x) is 60, the number of $10 tickets sold (y) is 60, and the number of $15 tickets sold (z) is 60.