Answer to Question #111037 in Algebra for Judy

Question

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.

Answer 1

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.

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

$25y-18y=12700-11223\\ 7y=1477\\ y=211\\ x=508-y=508-211=297$

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

Answer: 297 orchestra seats, 211 balcony seats