Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824.00 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
students tickets --- x
adult tickets --- 2x
solve:
3(2x) + 2x = 824
3(2x)+2x =824
6x+2x=824
8x=824
x=824/8
x=103
answer = 103
To solve this problem, let's assign variables to the unknown quantities. Let's call the number of adult tickets sold "A" and the number of student tickets sold "S".
Given that twice as many adult tickets were sold as student tickets, we can write the equation A = 2S.
Now, let's look at the total revenue from ticket sales. Adult tickets are sold for $3 each, so the revenue from adult tickets is 3A. Student tickets are sold for $2 each, so the revenue from student tickets is 2S. The total revenue from ticket sales is $824, so we can set up the equation 3A + 2S = 824.
Now we have a system of two equations:
A = 2S
3A + 2S = 824
We can solve this system using substitution or elimination method. For simplicity, let's use substitution method here.
Substitute the value of A from the first equation into the second equation:
3(2S) + 2S = 824
6S + 2S = 824
8S = 824
S = 824/8
S = 103
Now that we know S = 103, we can substitute this back into the first equation to find A:
A = 2 * 103
A = 206
So, 103 student tickets and 206 adult tickets were sold.