Exactly 120 tickets were sold for a concert. The tickets cost $\$ 12$ each for adults, $\$ 10$ each for seniors, and $\$ 6$ each for children. The number of adult tickets sold was equal to the number of child tickets sold. Given that the total revenue from the ticket sales was $\$ 1100$, the number of senior tickets sold was
(A) 110
(B) 20
(C) 40
(D) 2
(E) 18
Let the number of adult tickets sold be $a$.

Since the price for each adult ticket is $\$ 12$, then the revenue from all adult tickets sold (in dollars) is $12 \times a$ or $12 a$.

Since the number of child tickets sold is equal to the number of adult tickets sold, we can let the number of child tickets sold be $a$, and the total revenue from all $\$ 6$ child tickets be $6 a$ (in dollars).

In dollars, the combined revenue of all adult tickets and all child tickets is $12 a+6 a=18 a$.

Since the total number of tickets sold is 120, and $a$ adult tickets were sold and $a$ child tickets were sold, then the remaining $120-2 a$ tickets were sold to seniors.

Since the price for each senior ticket is $\$ 10$, then the revenue from all senior tickets sold (in dollars) is $10 \times(120-2 a)$.

Thus the combined revenue from all ticket sales is $10 \times(120-2 a)+18 a$, dollars.

The total revenue from the ticket sales was $\$ 1100$ and so $10 \times(120-2 a)+18 a=1100$.

Solving this equation, we get $10 \times 120-10 \times 2 a+18 a=1100$ or $1200-20 a+18 a=1100$ or $1200-2 a=1100$ and so $2 a=100$ or $a=50$.

Therefore, the number of senior tickets sold for the concert was

$120-2 a=120-2(50)=120-100=20$.

We may check that the number of tickets sold to each of the three groups gives the correct total revenue.

Since the number of adult tickets sold was equal to the number of child tickets sold which was equal to $a$, then 50 of each were sold.

The revenue from 50 adult tickets is $50 \times \$ 12=\$ 600$.

The revenue from 50 child tickets is $50 \times \$ 6=\$ 300$.

The revenue from 20 senior tickets is $20 \times \$ 10=\$ 200$.

The total revenue from all tickets sold was $\$ 600+\$ 300+\$ 200=\$ 1100$, as required.

ANSWER: (B)