Average movie prices in the United States are, in general, lower than in other countries. It would cost $80.43 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $76.32. How much does an average movie ticket cost in each of these countries?
Let's assume the cost of a movie ticket in the United States is x dollars.
According to the given information, 3 tickets in Japan plus 2 tickets in Switzerland cost $80.43.
Therefore, 3x + 2y = 80.43 ... (equation 1)
And, 3 tickets in Switzerland plus 2 tickets in Japan cost $76.32.
Therefore, 3y + 2x = 76.32 ... (equation 2)
To solve these two equations, let's multiply equation 1 by 2 and equation 2 by 3 to eliminate the x variable:
6x + 4y = 160.86 ... (equation 3)
9y + 6x = 228.96 ... (equation 4)
Now, subtract equation 3 from equation 4 to eliminate the x variable:
(9y + 6x) - (6x + 4y) = 228.96 - 160.86
9y + 6x - 6x - 4y = 68.1
5y = 68.1
y = 68.1 / 5
y ≈ 13.62
Now that we have the value of y, we can substitute it into equation 1 to find the value of x:
3x + 2y = 80.43
3x + 2(13.62) = 80.43
3x + 27.24 = 80.43
3x = 80.43 - 27.24
3x = 53.19
x = 53.19 / 3
x ≈ 17.73
Therefore, the average movie ticket cost in Japan is about $17.73, and the average movie ticket cost in Switzerland is about $13.62.