Martin was selling tickets for a basketball game in a high school. He sold 1,250 tickets and the total amount collected for the game was $2,750. The student tickets cost $2 each, and adult tickets cost $3 each. How many student and adult tickets were sold?

x = number of students tickets = 1,000

y = number of adults tickets = 250

Step-by-step explanation:

Let

x = number of students tickets

y = number of adults tickets

x + y = 1,250 (1)

2x + 3y = 2,750 (2)

Multiply (1) by 2

x + y = 1,250 (1) * 2

2x + 2y = 2,500 (3)

2x + 3y = 2,750 (2)

Subtract (3) from (2) to eliminate x

3y - 2y = 2,750 - 2,500

y = 250

Substitute y = 250 into (1)

x + y = 1,250

x + 250 = 1,250

x = 1,250 - 250

x = 1,000

x = number of students tickets = 1,000

y = number of adults tickets = 250