Question

PLEASE may I get help, I'm so lost. It would mean a lot to me, please.

A grade school is putting on its Spring show. The theater seats 120 people. Because of the demand for tickets, the school has made the following specifications:
•The number of tickets for children will be twice as many as the number for adults.
•Full-price adult tickets will be $24; children's tickets will be $12
•At least 10 of the adult tickets will be made available to seniors aged 60 and over at 25% discount
•Total ticket sales must be at least $1,800

1)How many children's tickets will be sold? 2)How many adult tickets (full-priced and senior) will be sold?
3)How many of the adult tickets can be sold with the senior discount?​

Answer 1

9514 1404 393

Answer:

1. 80
2. 40
3. 10 to 20, inclusive

Explanation:

1. The various goals can be met without filling the theater. This fact means there is a range of possibilities for each of the answers. However, we take the wording, "because of the demand for tickets ..." to mean demand is high and the theater will be sold out.

Since two children's tickets will be sold for each adult ticket sold, the number of children's tickets is 2/3 of the total.

children's tickets = 2/3 × 120 = 80

__

2. The remaining 40 tickets will be adult tickets.

40 adult tickets will be sold.

__

3. The total revenue must be at least $1800. If we allow 'd' tickets to be sold at a discount, then we can find the limits on d using the inequality ...

24(40-d) +24(0.75)d +12(80) ≥ 1800 . . . . revenue from ticket sales

-6d ≥ -120 . . . . . . . . . . . . . . . . . . . collect terms, subtract 1920

d ≤ 20 . . . . . . . . . . divide by -6

At least 10 and at most 20 adult tickets can be sold with a discount.

("At least 10" comes from the problem requirements.)