Question

all 12 seats in a hall were filled for a concert. the tickets cost $10 for adults and $6 for students the total proceeds were $980 how many adults and how many students attended the concert?

Answer 1

Let's denote the number of adults as A and the number of students as S. We have two equations based on the problem:

1. A + S = 12 (since all 12 seats were filled)

2. 10A + 6S = 980 (since the total proceeds were $980)

We can solve these equations simultaneously to find the values of A and S.

First, we can multiply the first equation by 6 to make the coefficients of S the same in both equations:

6A + 6S = 72

Then, we subtract this new equation from the second equation:

4A = 208

Solving this for A gives A = 52.

Substituting A = 52 into the first equation gives S = 12 - 52 = -40.

Therefore, the solution to the problem is A = 52 adults and S = -40 students.

However, the number of students cannot be negative, so there seems to be a mistake in the problem. The total proceeds of $980 cannot be reached with the given ticket prices and the number of seats. Please check the problem again.