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.

Question

Belen

Mathematics

31 October, 06:12

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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Answers (1)

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Starr · 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