Question

there were 508 people at a rock concert. Orchestra seats cost $25 per person and balcony seats cost $18. The amount sold totaled $11,223. Find the number of orchestra seats and the number of balcony seats sold for the concert.

Answer 1

211 balcony seats and 297 orchestra seats

Explanation:

x = Orchestra seats

y = Balcony seats

Total person at concert = 508

So x + y = 508

Cost

Orchestra seat $25x

Balcony seats $18y

Total money $11,223

So $25x + $18y = $11,223

Solving x + y = 508

$25x + $18y = $11,223

Solving the first equation for x and substituting x into the second equation then solve for y.

x + y = 508

x = 508 - y substituting x = 508 -y in second equation

25(508 - y) + 18y = 11,223

12700 - 25y + 18y = 11,223

12700 - 7y = 11223

-7y = 11223 - 12700

-7y = -1477

y = -1477 ÷ -7

y = 211 balcony seats

x + y = 508

x + 211 = 508

x = 508 - 211

x = 297 orchestra seats