Q:

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.

Accepted Solution

A:
Answer:300 teenagers Step-by-step explanation:Letx -----> the number of childreny ----> the number of teenagersz ----> the number of adultswe know thatx+y+z=1,200 ----> equation A4x+5y+6z=5,300 ---> equation By/x=3/8y=(3/8)x ----> equation CSubstitute equation C in equation A and equation B and solve for x,zx+y+z=1,200 ----> x+(3/8)x+z=1,200 ---> (11/8)x+z=1,200 -----> equation D4x+5y+6z=5,300 --> 4x+5(3/8)x+6z=5,300 --> (47/8)x+6z=5,300 --> equation ESolve 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 EThe solution is the intersection point both graphsThe intersection point is (800,100)see the attached figurethereforex=800 childrenz=100 adultsFind the value of yy=(3/8)x  ----> y=(3/8)800=300 teenagers