Question 32831
You have a great setup with variables.  
A=adult tickets
S=student tickets

Now, $3 for adults and $2 for students and when you add the number of tickets sold times the cost of the tickets you get $824. 
So you get 3A + 2S = 824

Then, the number of adult tickets sold is twice the amount of student tickets sold so  A = 2S

Now, we have two equations: 
3A + 2S = 824
A = 2S

Substitute (2S) in the top equation for (A) and solve:
3(2S) + 2S = 824

6S + 2S = 824
8S = 824
S= 103

Substitute back in to the other equation A = 2S
A= 2(103)
A=206

So the number of student tickets (S) is 103 and the number of adult tickets (A) is 206.  If you check your answers, the $ sold was $824 in tickets and the number of adult tickets is twice the amount of student tickets.