The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds

Question

The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling​ tickets, the members would like to raise $3900 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 600 seats are filled for a​ performance, how many of each type of ticket must have been sold for the members to raise exactly $3900 At one performance there were threethree times as many student tickets sold as adult tickets. If there were 480 tickets sold at that​ performance, how much below the goal of $3900 did ticket sales​ fall?

Answer 1

8.5d + 5.5s =3900

d+s = 480

5.5d + 5.5s = 600(5.5) = 3300

8.5d- 5.5d = 3900 -3300

3d = 600

d = 600/3 = 200 adult tickets

s= 600-200 =400 student tickets

but one night only 480 tickets were sold

d+s = 480

with 3 times as many student tickets sold as adult tickets

s = 3d

d+3d = 480

4d = 480

d = 480/4 = 120 adult tickets

s = 360 student tickets

8.5(120) + 5.5(360)

= 1020 + 1980

= $2,000

off their $3900 goal by $1900