It's the night of a home basketball game at your high school. You are sitting at a table, selling tickets. The tickets are on a roll; they are numbered. At the start, the first ticket you will sell is no. 831. You will charge adults $2 per ticket, and $1 for children up through 12 years old. The tickets all look alike on that roll. So as you sell a children's ticket you simply snip off a corner with scissors. That makes it clear that it's a child's ticket and can't be used as an adult ticket at the door to the gym. It's a foolproof system.
At the end, when the game begins, the number on the next ticket is no. 1131--thus you've sold exactly 300 tickets. And, incidentally, you have taken in $420.
Here's the question. You were very busy selling tickets to an impatient crowd, so you didn't keep track of how many tickets were adult tickets and how many were children's tickets. But now that things have quieted down, you can figure that out. Do so.
Solution
A bit of algebra does the trick:
Of course another solution technique is to count all the little triangular corners snipped off the children's tickets, assuming you can find them all.