word problems

Question

Four thousand tickets are sold for a football game. General admission tickets are $6 and reserved seats are $12 each. How many of each type of ticket are sold if the ticket sales are $33,000?

Answer 1

Hey Ang,

 

Let's assign a variable for the number of tickets of each type. G for general admission tickets and R for reserved seats.

 

G + R = 4000

 

We come up with a second equation for the total cost of both ticket types

 

6G + 12R = 33,000

 

Now solve the system of equations by using either elimination or substitution.

 

-6G - 6R = -24,000

 

Now add the second and third equations together.

 

6R = 9,000

 

R = 1,500

 

G = 2,500

 

2,500 general admission tickets and 1,500 reserved seats were sold. Hope this makes sense and good luck with questions of this type.

 

regards,

 

Mayuran

Answer 2

Let g be the number of general admission tickets sold, and r be the number of reserved tickets sold.

 

g + r = 4000         (1)

 

6g + 12r = 33,000  (2)

 

dividing equation (2) by 6;

 

g + 2r = 5500        (3)

 

from (1) g = 4000 - r

 

substitute this value in (3)

 

4000 - r + 2r = 5500; 

 

this gives r = 1500

 

hence g = 4000 - 1500 = 2500

 

checking; 6*2500 + 12 * 1500 = 33000 (proven)