Answer:
Admission fee charged = $3
Cost of each ride = $10
Step-by-step explanation:
Let admission fee charged by amusement park in dollars be =
Let cost of each ride in dollars be =
Given:
Admission plus four rides cost $22
If each ride cost in dollars = 
Cost of 4 rides in dollars will be = 
So, the total cost in dollars will be given as =
So, we have

Admission plus seven ride cost $31.
If each ride cost in dollars = 
Cost of 7 rides in dollars will be = 
So, the total cost in dollars will be given as =
So, we have

So, we have the system of equation as:
A) 
B) 
Solving the system by elimination method.
Eliminating
by subtracting equation A from B.

- 
- - - [Sign of each term of subtract-ant gets reversed]
-----------------------------

Dividing both sides by 3.

∴ 
Plugging in
in equation A.


Subtracting both sides by 12.

∴ 
Thus, admission fee charged = $3
Cost of each ride = $10