A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3203 tickets overall. It has sold 267 more $20 tickets than $10 tickets. The total sales are $62,610. How many tickets of each kind have been sold?
so, what have they told you?
If there are
x $10 seats
y $20 seats
z $30 seats, then
x+y+z = 3203
y = x+267
10x+20y+30z = 62610
Now just solve as usual for x,y,z
Post your work if you get stuck
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the number of $10 tickets sold is x.
The number of $20 tickets sold would then be x + 267, as it is given that 267 more $20 tickets were sold than $10 tickets.
The number of VIP tickets sold can be calculated by subtracting the sum of $10 and $20 tickets sold from the total number of tickets sold, which is 3203 - (x + x + 267) = 3203 - (2x + 267).
Now, let's calculate the total sales for each type of ticket:
The sales from $10 tickets would be $10 multiplied by the number of $10 tickets sold, which is 10x.
The sales from $20 tickets would be $20 multiplied by the number of $20 tickets sold, which is 20(x + 267) = 20x + 5340.
The sales from VIP tickets would be $30 multiplied by the number of VIP tickets sold, which is 30(3203 - (2x + 267)) = 30(3203 - 2x - 267) = 90390 - 60x.
According to the given information, the total sales are $62,610. So, we can set up the following equation:
10x + 20x + 5340 + 90390 - 60x = 62610.
Now, let's solve the equation for x:
10x + 20x + 5340 + 90390 - 60x = 62610
Combine like terms:
-30x + 95730 = 62610
Subtract 95730 from both sides:
-30x = -33120
Divide by -30:
x = 1104
Now that we have the value of x, we can substitute it back into our equations to find the number of each type of ticket sold:
Number of $10 tickets sold: x = 1104
Number of $20 tickets sold: x + 267 = 1104 + 267 = 1371
Number of VIP tickets sold: 3203 - (2x + 267) = 3203 - (2 * 1104 + 267) = 3203 - (2208 + 267) = 728.
Therefore, the number of $10 tickets sold is 1104, the number of $20 tickets sold is 1371, and the number of VIP tickets sold is 728.