Question

A movie theater sells tickets for $9 each, but students get a $3 discount. Yesterday, the movie theater, sold $590 tickets and collected a total of $4680. Determine how many tickets were sold to students.

Answer 1

210 tickets were sold to students

Solution:

Let "a" be the number of normal tickets sold at $ 9 each

Let "b" be the number of student ticket sold at $ 3 discount

Cost of 1 normal ticket = $ 9

Cost of 1 student ticket = $ 9 - $ 3 = $ 6

Yesterday, the movie theater, sold 590 tickets

Which means,

a + b = 590

a = 590 - b ---------- eqn 1

Yesterday, the movie theater,collected a total of $4680

Thus, we frame a equation as:

`a * 9 + b * 6 = 4680`

9a + 6b = 4680 --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

9(590 - b) + 6b = 4680

5310 - 9b + 6b = 4680

3b = 630

Divide both sides by 3

b = 210

Thus 210 student tickets were sold