SOLUTION: This question must be written in two unknowns for each problem and then solved each system by substitution. The question: tickets for a concert were sold to adults for $3 and to

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Question 32831: This question must be written in two unknowns for each problem and then solved each system by substitution.
The question: tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets were sold, then how many of each were sold?
I have been trying to do what the book says, but it is not helping.
What I have tried:
a=adults & s=students
$824=total of tickets
I got 204 adult tickets sold =$612
106 student tickets sold =$212
this provides the number of tickets sold of each, but I got that by deduction.
I am unsure of how to do the two equations and then solve them by substitution.
I Need help DESPERATLEY Thank you!

Answer by kietra(57) About Me  (Show Source):
You can put this solution on YOUR website!
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.