727 tickets were sold for a total of $5463. Student tickets were sold for $6 and nonstudent tickets were sold for $9. How many studnet tickets were sold?

Question

Algebra word problem

Answer 1

Let's say x is the number of student tickets sold. This would mean 5463=6x+9y(nonstudent tickets sold) OR we could express it as 5463=6x+9(727-x), because the total number of tickets was 727. working this out we simplify to 5463=-3x+6543 and then to -3x=-1080 or x=360. To check this answer we can simply plug the solution back in. 6*360+9*367=2160+3303=5463.

Answer 2

Let x = number of student tickets 

     y = number of nonstudent tickets

 

Then, x + y = 727

        6x +9y = 5463

 

Multiply the first equation by -6 to obtain the system:

 

-6x - 6y = -4362

 6x + 9y = 5463

 

Add the equations to get 3y = 1101.  So, y = 367.  Since x + y = 727 and y = 367, we have x = 727 - 367 = 360.

 

ANSWER:  360 student tickets were sold