Final answer:
By setting up a system of equations with adults and children ticket prices and solving for the number of tickets sold, we find that 78 adult tickets and 40 children tickets were sold. However, this doesn't match any of the given options, indicating a possible error in the question or calculations.
Step-by-step explanation:
To solve the question regarding how many adults and children attended the concert, we will need to set up a system of equations based on the given information and then solve these equations. We are given two types of tickets, for adults priced at $2.75 and for children at $1.5, and we know that 118 people altogether attended the concert, generating $275.75 in total.
Let A represent the number of adult tickets and C represent the number of children tickets. We have two equations:
- A + C = 118 (the total number of people)
- 2.75A + 1.5C = 275.75 (the total amount of money collected)
Now we solve the system:
From equation 1: A = 118 - C. We can substitute this in equation 2:
2.75(118 - C) + 1.5C = 275.75
325.5 - 2.75C + 1.5C = 275.75
Now, combine like terms:
-1.25C = -49.75
Divide by -1.25 to find the number of child tickets:
C = 49.75 / 1.25
C = 39.8 (Since we can't have a fraction of a ticket, C must be 40).
Using this value of C, we can find A:
A = 118 - C
A = 118 - 40
A = 78
Therefore, 78 adult tickets and 40 children tickets were sold, but this is not one of the provided options, meaning there may have been a mistake in the question or a miscalculation.
Since the answer does not match any of the options and we are not allowed to assume there was a typo, it would be recommended to double-check the question or seek clarification.