solving systems

Question

An auditorium sold 500 tickets for a play and raised $3400. Let x represent the number of adult tickets sold at $8 each and let y represent the number of student tickets sold at $5 each.  Write and solve a system of equations to determine the number of adult tickets and the number of student tickets that were sold.

Answer 1

8A + 5S = 3400

A + S = 500

2 equations 2 unknowns

eliminate one unknown and solve for the other

S=500-S

8A + 5(500-A) =3400

8A + 2500 -5A = 3400

3A = 3400-2500 = 900

A = 900/3= 300

S = 500-300 = 200

300(8) + 200(5) = 2400 +1000 = 3400