Question

Tickets for a play are $3 for students and $5 for non -students. On opening night, 937 tickets are sold and $3943 is collected. How many tickets were sold to students and non -students. Write a linear system and solve using the algebraic method of your choice.

Answer 1

371 to students and 566 to non- students

Explanation:

let s represent number of students and n represent non- students, then

s + n = 937 → (1) ← bases on tickets sold

3s + 5n = 3943 → (2) ← based on ticket sales

multiplying (1) by - 3 and adding to (2) will eliminate s

- 3s - 3n = - 2811 → (3)

add (2) and (3) term by term to eliminate s

(3s - 3s) + (5n - 3n) = 3943 - 2811

0 + 2n = 1132

2n = 1132 ( divide both sides by 2 )

n = 566

substitute n = 566 into (1) and solve for s

s + 566 = 937 ( subtract 566 from both sides )

s = 371

371 student tickets and 566 non- student tickets were sold