Question

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?

Answer 1

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:

• $3x+2y=80.95$,  (It would cost ​80.95 to buy three tickets in Japan + two tickets in Switzerland).

• $2x+3y=76.45$,  (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:

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

Step 4.

Replacing x in the second equation:

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

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:

$3(17.99)+2(13.49)=80.95$

$2(17.99)+3(13.49)=76.45$