the cost of one ticket is $1600 including service fee, but 5 tickets cost $7902, write the equation

Question

the cost of 1 ticket (including one time service fee) is $1600.00 and the cost of 5 tickets is $7902. write the equation

Answer 1

If s is the service fee and the cost of one ticket is t then the price p in dollars is given by:

p=s+nt where n is the number of tickets. When n=1, p=$1600, so:

1600=s+t and 7902=s+5t, therefore:

7902-1600=s+5t-s-t=4t,

6302=4t, and t=6302/4=$1575.50. So s, the service fee=1600-1575.50=$24.50.

The equation is p=24.50+1575.50n. (When n=1, p=24.50+1575.50=1600; when n=5, p=24.50+7877.50=7902.)

If you don't like algebra, the difference in the two prices must be the four tickets, so one ticket costs a quarter of this. We know the price including the service fee is $1600 so the service fee must be this less the price of a ticket.