Question

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.

Answer 1

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