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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.

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carlosego
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
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