A movie theater selks adult tickets for $12 and child tickets for $5. If theater sold 120 tickets for yesterday's matinee and earning a total revenue of $1,160.

Question

How many of each type of ticket did they sell?

Answer 1

This question gives you simultaneous equations in two unknown variables Adult tickets, and Child tickets.

theater sells adult tickets for $12 and child tickets for $5 earning a total revenue of $1,160

(1) 12A + 5C = 1160

theater sold 120 tickets for yesterday's matinee

(2) A + C = 120

METHOD 1: you can rearrange (2) so that A = 120 - C then substitute this for A in (1).

Hence 12(120 - C) + 5C = 1160

=> 1440 - 12C + 5C = 1160

=> -7C = 1160 - 1440 = -280

=> C = -280/-7 = 40

Then substitute C in (2) to get A + 40 = 120 => A = 80

METHOD 2: you can multiply (2) by 5 to get 5C and then subtract from (1) to eliminate C term...

12A + 5C = 1160

-

5A + 5C = 600

=

7A + 0C = 560

=> A = 560/7 = 80

now substitute A in (2) to get 80 + C = 120 => C = 40

Hence the theater sold 40 children's tickets and 80 adult tickets.

It's quick to double check: 80 x 12 + 40 x 5 = 960 + 200 = 1160 as required.