A community group bought 25 tickets to a play. Adult tickets cost $30 each and student tickets cost $20 each. In all, the group spent $620 on the tickets. Determine if each equation is a part of the system of equations that can be used to find the number of each type of ticket that was sold. The variable x represents the number of student tickets, and y represents the number of adult tickets.
What equations?
To determine if an equation is part of the system of equations that can be used to find the number of each type of ticket sold, we need to set up a system of equations based on the given information.
Let's assume the number of student tickets sold is represented by 'x' and the number of adult tickets sold is represented by 'y'.
Given:
-The community group bought 25 tickets in total. So, the total number of tickets sold is x + y = 25. This equation represents the total number of tickets sold.
-Adult tickets cost $30 each, so the cost of adult tickets is 30y.
-Student tickets cost $20 each, so the cost of student tickets is 20x.
-The group spent $620 on the tickets, so the total cost is 30y + 20x = 620. This equation represents the total cost of the tickets.
Therefore, the system of equations that can be used to find the number of each type of ticket sold is:
x + y = 25
30y + 20x = 620
Now, we can determine if each equation is a part of the system by comparing them to the equations we derived.
For the equation x + y = 25:
- This equation represents the total number of tickets sold, which is consistent with our derived equation. So, it is indeed a part of the system.
For the equation 30y + 20x = 620:
- This equation represents the total cost of the tickets, which is consistent with our derived equation. So, it is also a part of the system.
Therefore, both equations x + y = 25 and 30y + 20x = 620 are part of the system of equations that can be used to find the number of each type of ticket that was sold.