SOLUTION: the small soo at the park charges $12 for adult admission, $8 for child admission and $5 for senior admission. for one day, the zoo collected $839 and admitted 98 visitors. If the

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the small soo at the park charges $12 for adult admission, $8 for child admission and $5 for senior admission. for one day, the zoo collected $839 and admitted 98 visitors. If the       Log On


   

Question 148958: the small soo at the park charges $12 for adult admission, $8 for child admission and $5 for senior admission. for one day, the zoo collected $839 and admitted 98 visitors. If the adult admission is 5 more than the senior admission, how many persons of each category were admitted on this day?
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
x=number of adults
y=number of kids
z=number of seniors
coefficient=admission price

x=z+5
12x+8y+5z=839
x+y+z=98

Solve for y in the third equation
y=98-z-x
Plug in x
y=98-z-z-5

Plug in values for y and x in the second equation
12(z+5)+8(98-2z-5)+5z=839

Distribute
12z+60+784-16z-40+5z=839

Combine like terms
z+804=839

Subtract 804
z=35

number of seniors=35

x=z+5

Plug in z
x=35+5
x=40

number of adults=40

x+y+z=98
40+y+35=98

Combine like terms
75+y=98

Subtract 75 from both sides
y=23

number of kids=23

So,
# of seniors=35
# of adults=40
# of kids=23