19.0k views
4 votes
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?

User Teg
by
7.5k points

1 Answer

5 votes
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.
User Wesbos
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories