Question

The manager at a movie theater keeps track of the number of evening tickets and matinee tickets sold each day and the total money received. On Friday, a total of 63 tickets were sold, and the money collected was $742. If evening tickets are sold for $14 and matinee tickets are sold for $10, how many evening tickets and matinee tickets were sold?

Answer 1

Given:
63 tickets were sold.
Money collected = $742.
Evening tickets cost $14 each.
Matinee tickets cost $10 each.

Let
x = number of evening tickets sold
y = number of matinee tickets sold

Then
 x + y = 63                (1)
14x + 10y = 742       (2)

From (1), obtain
y = 63 - x                 (3)
Substitute (3) into (2).
14x + 10(63 - x) = 742
4x + 630 = 742
4x = 112
x = 28
y = 63 - 28 = 35

Answer:  28 evening and 35 matinee tickets were sold.