Question

Average movie prices in the unites States are, in general, lower than in other countries. it would cost $77.94 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $73.86. How much does an average movie ticket cost in each countires?Japan average:Switzerland average:

Answer 1

If "J" is the average price in Japan and "S" is the average price is "S", then since we are told that three tickets in Japan plus two tickets in Switzerland cost $77.94 we have the following relationship:

`3J+2S=77.94,\text{ (1)}`

We are also told that three tickets in Switzerland plus two tickets in Japan would cost $73.86. This gives us the following equation:

`2J+3S=73.86,(2)`

We get two equations with two variables. To solve this system we will multiply equation (1) by -2:

`-6J-4S=-155.88,(3)`

Now we multiply equation (2) by 3:

`6J+9S=221.58,(4)`

Now we will add equation (3) and equation (4):

`-6J-4S+6J+9S=-155.88+221.58`

Now we add like terms;

`5S=65.7`

Dividing both sides by 5:

`S=(65.7)/(5)=13.14`

Now we replace the value of S in equation (1):

`3J+2(13.14)=77.94`

Solving the operation:

`3J+26.28=77.94`

Subtracting 26.28 to both sides:

`\begin{gathered} 3J=77.94-26.28 \\ 3J=51.66 \end{gathered}`

Dividing both sides by 3:

`J=(51.66)/(3)=17.22`

Therefore, the average in Japan is $17.22 and the average in Switzerland is $13.14.