Question

the arlington drama club is selling tickets to an upcoming play. They can sell at most 250 tickets. The adult tickets for $15 each and student tickets costs $5 each. They would like to raise at least $2000. It x represents the number of adult tickets and y represents the number of student tickets.

Answer 1

Number of adult tickets = 75

Number of student tickets = 175

Solution:

Let x represents the number of adult tickets and

y represents the number of student tickets.

Total number of tickets sold = 250

⇒ x + y = 250 – – – – (1)

Cost of adult ticket = $15

Cost of student ticket = $5

Total cost of collection = $2000

15x + 5y = 2000 – – – – (2)

Multiply equation (1) by 5

⇒ (1) × 5  5x + 5y = 1250 – – – – (3)

Subtract equation (3) from equation (2), we get

15x + 5y – 5x – 5y = 2000 – 1250

⇒ 10x = 750

⇒ x = 75

Substitute x = 75 in equation (1), we get

⇒ 75 + y = 250

⇒ y = 250 – 75

⇒ y = 175

Number of adult tickets = 75

Number of student tickets = 175