the members of the city cultural center have decided to put on a play once a night for a week. their auditorium holds 500 people. by selling tickets, the members would like to raise $3050 every night to cover all expenses. let d represent the number of adult tickets sold at $8.50. let s represent the number of student tickets sold at $5.50 each. if all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3050? at one performance there were twotwo times as many student tickets sold as adult tickets. if there were 360 tickets sold at that performance, how much below the goal of $3050 did ticket sales fall? the members adult tickets tickets

In first question, Number of student's ticket(s) = 400

And number of adult's ticket(d) = 100

In second question, The goal of $3050 fell by $710

Step-by-step explanation:

1. Since, Here d represents the number of adult tickets and s represents the number of student tickets.

And, all 500 seats are filled for a​ performance.

Therefore, s + d = 500 (1)

Also, the price of one adult's  ticket = $8.50

The price of one student's ticket= $5.50

And, their is a revenue of $3050 by selling the tickets.

Thus, 8.50 d + 5.50 s = 3050 (2)

By solving the equation (1) and equation (2),

we get, s = 400, d=100

Thus, Number of student's ticket(s) = 400

And number of adult's ticket(d) = 100

2. According to the question,

s = 2 d   (3)

s + d = 360 (4)

By solving equation (3) and (4),

We get, s = 240 and d = 120

thus, the total revenue after selling 360 tickets = 8.50 × 120 + 5.50 × 240 = $2340

But, the goal is $3050 ( according to the question)

Thus the total fall = 3050 - 2340 = $710

the answer is 375 miles

step-by-step explanation:

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