Drama club question algebra 1

Question

The Drama Club recieves $388 by selling 304 tickets to the opening night of the opera. If the full price of a ticket is $2.50 and discount tickets for students and seniors are $0.50 each, how many full-price tickets were sold

Answer 1

2.5x + 0.5y = 388 OR 5x + y = 388...I prefer the second version because it is simpler.

5x + y = 388 AND x + y = 304

so you make the two equations as similar as possible

y = 388 - 5x AND y = 304 - x

now you set the equations equal to each other and solve for x

304 - x = 388 - 5x

304 + 4x = 388

4x = 388 - 304

4x = 84

x = 21

now you plug the x-value into one of the original equations and solve for y

x + y = 304

21 + y = 304

y = 283

x = 21, y = 283, so there were 21 regular tickets and 283 discount tickets sold.