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Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost ​80.95 to buy three tickets in Japan + two tickets in Switzerland. Three tickets in Switzerland + two tickets in Japan would cost ​76.45. How much does an average movie ticket cost in each of these​ countries?

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Answer:

In Japan a movie ticket has a price of 17.99, and in Switzerland has a price of 13.49.

Step-by-step explanation:

Step 1.

  • Let x be the price of a movie ticket in Japan
  • Let y be the price of a movie ticket in Switzerland

Step 2.

According with the description:

  • [tex]3x+2y=80.95[/tex],  (It would cost ​80.95 to buy three tickets in Japan + two tickets in Switzerland).
  • [tex]2x+3y=76.45[/tex],  (Three tickets in Switzerland + two tickets in Japan would cost ​76.45).

Step 3.

The two equations of step 2 can be used to solve both x and y. From the first equation, solving x:

[tex]x=\frac{80.95-2y}{3}[/tex].

Step 4.

Replacing x in the second equation:

[tex]2*\frac{80.95-2y}{3}+3y=76.45[/tex].

Solving for y (price in Switzerland):

[tex]y=13.49[/tex]

Step 5.

Using the found value of y to solve for x (price in Japan):

[tex]x=\frac{80.95-2(13.49)}{3}=17.99[/tex]

Step 6.

Then it is possible to check that:

[tex]3(17.99)+2(13.49)=80.95[/tex]

[tex]2(17.99)+3(13.49)=76.45[/tex]

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