Answer:
x represents the number of $16 category tickets sold and represents the number of $41 category tickets sold.
the total capacity of the concert hall is 13,000 seats, so the total number of tickets sold must equal 13,000:
x + y = 13,000
Second, we also know that each ticket in the $16 category earns $16 and each ticket in the $41 category earns $41. Total ticket sales revenues must equal the total capacity multiplied by the price of tickets in each category:
16x + 41y = 13.000 * 16 + 13.000 * 41
Let’s simplify this equation:
16x + 41y = 208.000 + 533.000
16x + 41y = 741,000
Now we have a system of equations:
x + y = 13,000
16x + 41y = 741,000
We can solve this system of equations to find the values of x and y. However, it is important to note that there may be several combinations of notes that satisfy these equations. One possible solution is:
x = 8.000
y = 5.000
So to fill all the seats in the concert hall, we would have to sell 8,000 tickets in the $16 category and 5,000 tickets in the $41 category.