Question

Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost ​$78.73 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost ​$75.02. How much does an average movie ticket cost in each of these​ countries?

Answer 1

Average movie ticket cost in Japan = $17.23

Average movie ticket cost in Switzerland = $ 13.52

Step-by-step explanation:

Let x be the cost of movie ticket in Japan and y be the cost of movie ticket in Switzerland.

Given 3 ticket in Japan + 2 tickets in Switzerland = $78.73

              ⇒ 3x + 2y = 78.73 – – – – (1)

Given 3 ticket in Switzerland + 2 tickets in Japan = $75.02

              ⇒ 3y + 2x = 75.02

              ⇒ 2x + 3y = 75.02– – – – – (2)

Now, to solve (1) and (2), we multiply equation (1) by 2 and equation (2) by 3.

(1) × 2 ⇒       6x + 4y = 157.46 – – – – (3)

(2) × 3 ⇒       6x + 9y = 225.06 – – – – (4)

Subtract (3) from (4), we get

6x + 9y – (6x + 4y)= 225.06 – 157.46

⇒ 6x + 9y – 6x – 4y= 67.6

⇒ 5y = 67.6

⇒ y = 13.52

Now substitute y = 13.52 in equation (1), we get,

(1) ⇒ 3x + 2(13.52) = 78.73

⇒ 3x = 78.73 – 27.04

⇒ x = 27.23

Hence, Average movie ticket cost in Japan is $27.23

Average movie ticket cost in Switzerland is $ 13.52.