Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar ly
ing on the floor next to it. She said, I wonder whether the dollar belongs inside the cash box or not. The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not? (justify/defend)
which one checks as in the other solution does not have a solution in non-negative integers. On the other hand, the analogous system
s + 2c = 47
5s+8c = 201
with solution s=13 and c=17. So, as in the other solution, we conclude that the extra dollar belongs in the cash box, with 13 singles and 17 couples attending the dance.
