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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

​$3,300

every night to cover all expenses. Let d represent the number of adult tickets sold at

​$7.50.

Let s represent the number of student tickets sold at

​$4.50

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

​$3,300​?

At one performance there were

three

times as many student tickets sold as adult tickets. If there were

400

tickets sold at that​ performance, how much below the goal of

​$3,300

did ticket sales​ fall?

Answer 1

200 adults + 400 students will get $3,300

if s =3d and a or d + s = 400

d+s = 400

d = 400-s

7.5d + 4.5s =

7.5d + 4.5(3d)=

7.5d + 13.5d =

21 d =400

d = 400/21 = about 19 adults

s = 400-s = about 381 students

7.5(19) + 4.5(381)

= 142.5 + 1714.5

=1857

3300-1857 = about $1443 short of the goal

give or take a little for rounding errors