word problems

Question

Five hundred more general admission tickets are sold than reserve seat tickets for a concert. If the general admission tickets are $10 each and the reserve tickets are $25 each, find the number of each type of ticket sold if the ticket sales are $40,000?

Answer 1

Let x = the number of reserve seat tickets sold. Then the number of general admission tickets can be expressed as (x + 500). We can form the following equation from the info given in the problem:

 

10(x + 500) + 25x = 40000

 

You should be able to now solve this linear equation for x, Ang. This will enable you to determine how many of each type of ticket were sold.

Answer 2

Let g = # general admission tickets

Let r = # reserve seat tickets

 

Ticket Sales = 10(#general adm tickets)+25(reserve tickets):

 

10g + 25r = 40,000 _____ eqn 1

 

500 more general adm tickets were sold than reserve:

 

g = r + 500 _____ eqn 1

 

Substitute r + 500 in 1st equation and solve for r

 

10(r+500) + 25r = 40,000

 

Once you solve for r, # reserve tickets, then add 500

to that to get the number of general admission tickets.