Question

Please help ASAP. Thanks!

A concert hall has 13,000 seats and two categories of ticket prices, \( \$ 16 \) and \( \$ 41 \). Assume that all seats in each category can be sold. a. How many tickets of each category should be sol

Answer 1

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.