Answer:
<u>875</u> student tickets were sold.
Step-by-step explanation:
Given:
The drama club sold 2100 tickets to their last play.
Student tickets were $5 and adult tickets were $7.
They collected $12,950.
Now, to find the number of student tickets sold.
Let the number student tickets be ![x.](https://tex.z-dn.net/?f=x.)
And the number adult tickets be ![y.](https://tex.z-dn.net/?f=y.)
So, the total number of tickets:
![x+y=2100\\y=2100-x](https://tex.z-dn.net/?f=x%2By%3D2100%5C%5Cy%3D2100-x)
Now, the total amount collected:
![5x+7y=12950](https://tex.z-dn.net/?f=5x%2B7y%3D12950)
Putting the value of
from above:
![5x+7(2100-x)=12950](https://tex.z-dn.net/?f=5x%2B7%282100-x%29%3D12950)
![5x+14700-7x=12950](https://tex.z-dn.net/?f=5x%2B14700-7x%3D12950)
![14700-2x=12950](https://tex.z-dn.net/?f=14700-2x%3D12950)
<em>Subtracting both sides by 14700 we get:</em>
![-2x=-1750](https://tex.z-dn.net/?f=-2x%3D-1750)
<em>Dividing both sides by -2 we get:</em>
![x=875.](https://tex.z-dn.net/?f=x%3D875.)
The number of student tickets = 875.
Therefore, 875 student tickets were sold.