the drama club receives $3,301 by selling 376 tickets to the opening night of the musical. if the full price of a ticket is $10.75 and discount tickets for students and seniors are $6 each how many discounted senior student tickets were sold

156 senior/student tickets were sold.

Step-by-step explanation:

Create a system of equations (I used 'x' for full price people and 'y' for senior/students)

10.75x + 6y = 3,301

x + y = 376

Then solve for one variable by moving one variable to the right on the second equation:

x + y = 376 to x = 376 - y

Now plug that new equation into the first equation, where the 'x' is.

10.75 (376 - y) + 6y = 3,301

Distribute 10.75 into the parentheses:

4,042 - 10.75y + 6y = 3,301

Now combine like terms:

4,042 - 4.75y = 3,301

Move 4,042 to the right to combine with 3,301:

4,042 - 4,042 - 4.75y = 3,301 - 4,042

-4.75y = - 741

Now divide both sides by - 4.75:

-4.75y/-4.75 = - 741/-4.75

y = 156

156 senior/student tickets!