Question

 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 sold___ adult tickets and_____student tickets

Answer 1

Answer: 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