Final answer:
Without additional information about the number of friends, options A) 12 tickets and B) 14 tickets both evenly divide 84, making them both correct. The exact answer from those provided cannot be determined with the information given.
Step-by-step explanation:
Solving the Ticket Sale Problem
Let us denote the number of friends that Matt has as x. Since Matt and his x friends all sold the same number of tickets, and they sold 84 tickets in total, we can set up the equation x + 1 (Matt plus his friends) times the number of tickets t equals 84. Therefore, the equation would be (x + 1) \(\cdot\) t = 84. Since we are not given the exact number of friends, we cannot determine the value of x or t from the information provided. However, to find the answer from the options given, we need to check which option divides evenly into 84, as this represents the number of tickets each person sold.
By checking each option:
- A) 12 tickets would mean 84 / 12 = 7 people (Matt plus 6 friends), which works.
- B) 14 tickets would mean 84 / 14 = 6 people (Matt plus 5 friends), which works.
- C) 16 tickets would mean 84 / 16 is not a whole number, so it doesn't work.
- D) 10 tickets would mean 84 / 10 is not a whole number, so it doesn't work.
So the answer is either A) 12 tickets or B) 14 tickets. Without additional information about the number of friends, we cannot determine the exact answer. For the purpose of the given options, the question as it is does not allow us to determine a single correct answer from those provided.