Answer:
general admission tickets 1170
courtside tickets 985
tickets bench seats. 130
Step-by-step explanation:
To solve the problem, it is necessary to generate a system of equations with the information provided by the statement.
First be
x = # general admission tickets
y = # courtside tickets
z = # tickets bench seats.
The first equation would be that they sold nine times more general admission tickets than bench seats tickets.
That is: x = 9 * z (1)
And the second equation is that the number of general admission tickets sold was 55 more than the sum of the number of courtside tickets and bench seats tickets.
That is: x = 55 + y + z (2)
Now the third equation would be the money raised.
28 * x + 43 * y + 173 * z = 97605 (3)
Now if I replace I rearrange (1):
z = x / 9 (4) and replacement in 2, I have:
x = 55 + y + x / 9, rearranging:
y = (8/9) * x - 55 (5)
Now replacing (4) and (5) in 3, we have:
28 * x + 43 * ((8/9) * x - 55) + 173 * (x / 9) = 97605
Solving the above:
x = 1170, therefore
y = (8/9) * 1170 55 = 985
z = 1170/9 = 130
We can confirm this with equation (3)
28 * x + 43 * y + 173 * z = 97605
28 * 1170 + 43 * 985 + 173 * 130 = 97605
