A movie theater has 400 seats. Tickets at the theater cost $8 for students, $10 for adults, and $7 for senior citizens. On a night when all the seats were sold, the theater made $3,535 from ticket sales. If the number of adult tickets sold was 10 less than the number of student and senior tickets combined, how many senior tickets were sold?

A.) 55

B.) 150

C.) 195

D.) 255

We are asked to solved for how many senior citizens tickets were sold. Solving this requires us to generate an expression that calculates 3 unknown variables which are students (S), adults (A), Senior Citizen (C). On the first condition, we can generate the first expression. It is stated in the problem that "all seats are sold". So for the first expression, we have

(1) S+A+C=400

We can express the second equation by using the cost of each ticket of the students (S), adults (A) and Senior Citizen (C). The theater made a $3535, so (2) 8S+10A+7Z=3535

and for the last expression, it is stated "If the number of adult tickets sold was 10 less than the number of student and senior tickets combined". Translating this to an expression, we have

(3) A = (S+C) - 10

Rearranging to standard form the third expression,

S+C-A=10 We can solve this since we have 3 expressions and 3 variables. Using an online 3 x 3 equation solver.

We have the answer for the number of

Student (S) = 150

Adults (A) = 195

Senior Citizen (C) = 55

So, the Final Answer is 55