Final answer:
To determine the number of adults and students who attended the play, we set up two equations: A + S = 950 and 2A + S = 1200. Solving the system, we find that 250 adults and 700 students attended the play.
Step-by-step explanation:
To solve the problem of determining how many adults and students attended the school play, we need to set up a system of equations based on the given information. There are two unknowns: the number of adult tickets (A) and the number of student tickets (S). We are given that adult tickets cost $2 each, and student tickets cost $1 each. We also know that a total of 950 people attended and that the total ticket sales amounted to $1200.
The first equation represents the total number of attendees: A + S = 950.
The second equation represents the total amount of ticket sales: 2A + S = 1200.
To solve the system of equations, we can use either substitution or elimination method. Using the elimination method, we can multiply the first equation by -1 to help us eliminate S when we add the two equations together:
- -1(A + S) = -1(950)
- -A - S = -950
Adding this to the second equation:
- (2A + S) + (-A - S) = 1200 - 950
- A = 250
Now we know there were 250 adult tickets sold. We can substitute A with 250 in the first equation to find S:
- 250 + S = 950
- S = 950 - 250
- S = 700
Therefore, 250 adults and 700 students attended the school play.