Sophia was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a $5 bill
lying 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 $10 (for individuals) or 2 tickets for $15 (for couples). She looked inside the cash box and found $590 and ticket stubs for the 68 students in attendance. Does the $5 bill belong inside the cash box or not? Be sure to show all work and explain your reasoning using complete sentences.
The first thing we will do in this case is to define variables: x = number of individual tickets. y = number of tickets per couple. We have then that the system of equations that represents the problem is: 10x + 15y = 590 x + 2y = 68 Solving the system we have: x = 32 y = 18 Substituting we have: 10 (32) + 15 (18) = 590 320 + 270 = 590 590 = 590 Equality is met, therefore the $ 5 bill belongs to the box. Answer: the $ 5 bill belong inside the cash box
