Question

Thomas was selling tickets to his school play. The tickets cost $5.00 for adults and $2.00 for children. He sold 200 tickets and collected $610. Which system represents the number of adult and child tickets that Thomas sold?

Answer 1

adult: $5, qty x
children: $2, qty y
total: $610, qty 200

Cost: 5x + 2y = 610
Quantity: x + y = 200

Using elimination method to solve the system of equations:
1(5x + 2y = 610) → 5x + 2y = 610
-2( x + y = 200) → -2x - 2y = -400
Add both equations: 3x + 0 = 210
Divide both sides by 3: x = 70

Substitute "x = 70" into either the Cost or Quantity equation:
Quantity: x + y = 200 → 70 + y = 200 → y = 130

Adult tickets sold = 70
Children tickets sold = 130