Word Problem Linear Systems

Question

The cost of a ticket to the circus is $19.00 for children and $34.00 for adults. On a certain day, attendance at the circus was 500 and the total gate revenue was $14,000. How many children and how many adults bought tickets?

 

The number of children was (_______) and the number of adult was (_________)

Answer 1

Let x = the number of children's tickets

Let y = the number of adult tickets

x + y = 500       x = 500 - y

19x + 34y = 14000

19(500 - y) + 34y = 14000

9500 - 19y + 34y = 14000

15y = 4500

y = 300 adult tickets

x = 500 - 300

x = 200 child tickets