Question

Tickets to the zoo cost four dollars for Children, five dollars for teenagers and six dollars for adults. In the high season, 1200 people came to the zoo every day. On a certain day, the total revenue at the zoo was $5300. For every three teenagers, eight children went to the zoo. How many teenagers went to the zoo.

Answer 1

300 teenagers

Explanation:

Let

x -----> the number of children

y ----> the number of teenagers

z ----> the number of adults

we know that

x+y+z=1,200 ----> equation A

4x+5y+6z=5,300 ---> equation B

y/x=3/8

y=(3/8)x ----> equation C

Substitute equation C in equation A and equation B and solve for x,z

x+y+z=1,200 ----> x+(3/8)x+z=1,200 ---> (11/8)x+z=1,200 -----> equation D

4x+5y+6z=5,300 --> 4x+5(3/8)x+6z=5,300 --> (47/8)x+6z=5,300 --> equation E

Solve the system of equations D and equation E by graphing

(11/8)x+z=1,200 -----> equation D

(47/8)x+6z=5,300 --> equation E

The solution is the intersection point both graphs

The intersection point is (800,100)

see the attached figure

therefore

x=800 children

z=100 adults

Find the value of y

y=(3/8)x ----> y=(3/8)800=300 teenagers