### Instruction: A movie theater seats $100$ patrons. The theater is full for the 5:00 pm Saturday movie. Adult tickets sell for $\$9.00$ each and children's tickets sell for $\$5.00$ each. If the theater collected $\$640$ in ticket sales for the 5:00 pm Saturday show, how many children's tickets were sold?### Response: I need to find out how many children's tickets were sold, so I'll call that number $x$.
Then, the number of adult tickets sold must be $100 - x$, since the theater is full and there are $100$ seats.
The total ticket sales are $\$640$, so I can write an equation that relates the number of tickets sold and the prices: $9(100 - x) + 5x = 640$.
To solve for $x$, I'll simplify and rearrange the equation: $900 - 9x + 5x = 640$, $-4x = -260$, $x = 65$.
This means that 65 children's tickets were sold.