Question

There are 257 people at a dance performance. Orchestra seats cost $12 and balcony seats cost $8. The total receipts were $2,716. Find the number of orchestra seats and the number of balcony seats sold for the performance.

Answer 1

x = # of balcony seats

y = # of orchestra seats

We have to create a system of equations to solve this problem

x + y = 256

$8x + $12y = $2,716

We will solve this system of equations by elimination.

Multiply the first equation by -8

-8x - 8y = -2048

8x + 12y = 2716

Let's add the equations together

0 + 4y = 668

Simplify the left side

4y = 668

Divide both sides by 4

y = 167

We can subtract 167 from 257 to get the number of balcony seats.

257 - 167 = 90 balcony seats

There are 167 orchestra seats and 90 balcony seats