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Zanzabum
3 years ago
6

Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost ​80.95 to buy three ti

ckets 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?
Mathematics
1 answer:
densk [106]3 years ago
5 0

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.

  • <em>Let x be the price of a movie ticket in Japan</em>
  • <em>Let y be the price of a movie ticket in Switzerland</em>

Step 2.

According with the description:

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

Step 3.

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

x=\frac{80.95-2y}{3}.

Step 4.

<em>Replacing x in the second equation</em>:

2*\frac{80.95-2y}{3}+3y=76.45.

Solving for y (price in Switzerland):

y=13.49

Step 5.

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

x=\frac{80.95-2(13.49)}{3}=17.99

Step 6.

Then it is possible to check that:

3(17.99)+2(13.49)=80.95

2(17.99)+3(13.49)=76.45

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