Math word problems giving me a major headache any help?

Question

 Trevor's school is selling tickets to a play. On the first day of ticket sales the school sold 1 senior citizen ticket and 12 child tickets for a total of $182. The school took in $252 on the second day by selling 10 senior citizen tickets and 8 child tickets. Find the price of a senior citizen ticket.

Answer 1

Let the x represent the number of senior tickets and y represent the number of child tickets. Thus1 senior ticket + 12 child tickets = $182 becomes:

x + 12y = 182

and for day 2:

10x + 8y = 252

We now have 2 equations with 2 unknowns and can solve using any method, for instance by substitution:

x + 12y = 180 -> x = 182 - 12y

10x + 8y = 252 -> 10(182 - 12y) + 8y = 252

1820 - 120y + 8y = 252

- 120y + 8y = -1568

-112y = -1568

y = 14

back substituting:

x = 182 - 12(14)

x = 182 - 168

x = 14

So, both the senior and child tickets cost $14.