Question

University theatre sold 414 tickets for a play. Tickets cost $20 per adult and $13 per senior citizen. If total receipts were $6173, how many senior citizens tickets were sold?

Answer 1

Let's set variables to the different tickets:
S is senior tickets, and A is adults.

If there were 414 tickets sold, then
414 = A + S

If the total amount sold was $6173 and adults tickets were $20 and senior tickets were $13, then
6173 = 20A + 13S

We can then put these two equations into a system of equations:
$414 = a +s\\ 6173 = 20a + 13s$
We can single out one of the variables in the simpler equation to solve for the other:
$414 = a + s \\ 414 - s = a$
Now that we have A, we can plug it into the other equation:
$6173 = 20a + 13s\\ 6173 = 20(414 - s) + 13s \\ 6173 = 8280 - 20s + 13s\\ - 2107 = - 7s \\ 301 = s$
We plug in 414 - S for A, then we factor in the 20. Then we subtract 8280 from both sides and combine the two Ss. Then we divide both sides by -7.

The theatre sold 301 senior tickets and 113 adult tickets.