Question

Tickets for admission to a high school football game cost $3 for students and $5 for adults. During 1 game, $2995 was collected from the sale of 729 tickets. Write & solve a system of equations to find the number of student tickets, x, and number of adult tickets, y, sold.

Answer 1

Number of student tickets = 325

Number of adult tickets = 404

Explanation:

Let,

x be the number of student tickets

y be the number of adult tickets

According to given statement;

x+y=729 Eqn 1

3x+5y=2995 Eqn 2

Multiplying Eqn 1 by 3

3(x+y=729)

3x+3y=2187 Eqn 3

Subtracting Eqn 3 from Eqn 2

(3x+5y)-(3x+3y)=2995-2187

3x+5y-3x-3y=808

2y=808

Dividing both sides by 2

`(2y)/(2)=(808)/(2)\\y=404`

Putting y=404 in Eqn 1

x+404=729

x=729-404

x=325

Hence,

Number of student tickets = 325

Number of adult tickets = 404