Adult tickets to a play cost $2.25 each and student tickets cost $1.75 each. Suppose there are twice as many student tickets sold as adult tickets. If the income from the play was $1,150, how many of each type of ticket were sold?
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the number of adult tickets as "A" and the number of student tickets as "S".
From the given information, we have the following equations:
1) The cost of an adult ticket: A * $2.25
2) The cost of a student ticket: S * $1.75
3) The total number of tickets sold: A + S
4) The total income from the play: $1,150
Using this information, we can form the equation:
(A * $2.25) + (S * $1.75) = $1,150
Now, we also know that there were twice as many student tickets sold as adult tickets (S = 2A).
Substituting S = 2A into our equation, we get:
(A * $2.25) + (2A * $1.75) = $1,150
Now we can solve this equation for A.
2.25A + 3.50A = 1,150
5.75A = 1,150
A = 1,150 / 5.75
A = 200
Therefore, 200 adult tickets were sold.
Substituting this value back into S = 2A, we find:
S = 2 * 200
S = 400
Therefore, 400 student tickets were sold.
So, there were 200 adult tickets and 400 student tickets sold.
A = 2S
2.25A + 1.75S = 1150
Substitute 2S for A and solve for S, then A.