Let x represent the number of adult tickets sold.
Let y represent the number of student tickets sold.
We were told that the movie theater sold a total of 205 tickets to a movie. This means that
x + y = 205
Adult tickets were $9 and student tickets were $5. This means that the cost of x adult tickets and y student tickets is 9x + 5y. If the total cost of the tickets was $1621, it means that
9x + 5y = 1621
From the first equation, x = 205 - y
We would substitute x = 205 - y into 9x + 5y = 1621. Thus, we have
9(205 - y) + 5y = 1621
1845 - 9y + 5y = 1621
- 9y + 5y = 1621 - 1845
- 4y = - 224
y = - 224/- 4
y = 56
x = 205 - y = 205 - 56
x = 149
Thus, 56 student tickets were sold
