Question 148958
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