members of the city cutrual

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 ​$3,350 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 ​$3,350​? At one performance there were two times as many student tickets sold as adult tickets. If there were 300 tickets sold at that​ performance, how much below the goal of ​$3,350 did ticket sales​ fall?

Answer 1

8.5d + 5.5s =3350

d+s=500

s=500-d

8.5d +5.5(500-d) = 3350

8.5-5.5d = 3350-5.5(500)

3d = 3350-2750= 600

d= 200 adult tickets

s= 300 student tickets

s=2d

d+s=300=3d

d=100

8.5d +5.5(300-d)=3(100)+1650=1950

3350-1950=$1400 short