Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $8.24 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
Total receipts = $8.24? Are you sure?
oops, sorry my error total receipts $824
Ticket 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 as student tickets
To solve this problem, we can break it down into steps:
Step 1: Assign variables to represent the unknown quantities.
Let's assign variables for the number of adult tickets and the number of student tickets. Let A represent the number of adult tickets, and S represent the number of student tickets.
Step 2: Set up equations for the given information.
From the problem statement, we know that the total receipts from ticket sales were $8.24. To determine the total amount from adult tickets and student tickets, we can set up the following equation:
3A + 2S = 8.24
We also know that there were twice as many adult tickets sold as student tickets. So we can set up another equation:
A = 2S
Step 3: Solve the system of equations.
Now we can substitute the value of A from the second equation into the first equation:
3(2S) + 2S = 8.24
6S + 2S = 8.24
8S = 8.24
S = 1.03
Now that we have the number of student tickets, we can substitute this value back into the second equation to find the number of adult tickets:
A = 2(1.03)
A = 2.06
Therefore, there were 2.06 adult tickets sold (which we can round down to 2 since we can't sell a fraction of a ticket) and 1.03 student tickets sold (which we can round up to 2).
So, there were 2 adult tickets and 2 student tickets sold.