Answer to Question #111037 in Algebra for Judy

Question #111037
There were 508 people at a choral concert. Orchestra seats cost $25 each and a balcony seats cost $18 each. The total receipts were $11,223. Find the number of orchestra seats and the number of balcony seats sold for the concert.
1
Expert's answer
2020-04-21T13:08:19-0400

Assume that there are "x" orchestra seats and "y" balcony seats. There are "x+y" seats sold for 508 people. Orchestra seats cost $25 so all orchestra seats cost $"25x" , balcony seat costs $18 and all balcony seats cost $"18y" . The total receipts were $"(25x+18y)" which are $11,223. Let's make system of equasions.

"\\begin{cases}\n x+y=508\\\\\n 25x+18y=11223\n\\end{cases}" "\\begin{cases}\n 25x+25y=12700\\\\\n 25x+18y=11223\n\\end{cases}"


"25y-18y=12700-11223\\\\\n7y=1477\\\\\ny=211\\\\\nx=508-y=508-211=297"


So, there are 297 orchestra seats and 211 balcony seats.

Answer: 297 orchestra seats, 211 balcony seats


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