Question

An amusement park charges admission plus a fee for each ride. Admission plus four ride cost $22. Admission plus seven ride cost $31. What is the charge for admission and the cost for each ride

Answer 1

Admission fee charged = $3

Cost of each ride = $10

Explanation:

Let admission fee charged by amusement park in dollars be =
`x`

Let cost of each ride in dollars be =
`y`

Given:

Admission plus four rides cost $22

If each ride cost in dollars =
`y`

Cost of 4 rides in dollars will be =
`4y`

So, the total cost in dollars will be given as =
`x+4y`

So, we have

`x+4y=22`

Admission plus seven ride cost $31.

If each ride cost in dollars =
`y`

Cost of 7 rides in dollars will be =
`7y`

So, the total cost in dollars will be given as =
`x+7y`

So, we have

`x+7y=31`

So, we have the system of equation as:

A)
`x+4y=22`

B)
`x+7y=31`

Solving the system by elimination method.

Eliminating
`x` by subtracting equation A from B.

`x+7y=31`

-
`x+4y=22`

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

-----------------------------

`3y=9`

Dividing both sides by 3.

`(3y)/(3)=(9)/(3)`

∴
`y=3`

Plugging in
`y=3` in equation A.

`x+4(3)=22`

`x+12=22`

Subtracting both sides by 12.

`x+12-12=22-12`

∴
`x=10`

Thus, admission fee charged = $3

Cost of each ride = $10