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

Answer:

Admission fee charged = $3

Cost of each ride = $10

Step-by-step 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.

$\frac{3y}{3}=\frac{9}{3}$

∴ $y=3$

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