Question

A cinema hall has three classes of tickets namely classic, deluxe and economy. Classic is priced at 250 per ticket, deluxe at 200 per ticket and economy at 150 per ticket. The number of deluxe class tickets was fifty more than that of the classic class and 100 less than that of the economy class. If the total amount collected on a particular day was 77500 find the number of tickets sold of each class.

Answer 1

let no. of classic tickets be x, no. of economy tickets be y and no. of deluxe tickets be z.
now,
no. of deluxe tickets z=x+50=y-100
that gives y-x=150.-1
now, if total amount is 77500,
250x+150y+200z=77500
this gives
5x+3y+4z=1350.
now,z=x+50
so,
9x+3y=1150.
this gives
3x+y=350.-2
now using 1 and 2,
4x=200
x=50.
y=x+150=200.
z=x+50=100.