Answer:
Let's denote the cost of one movie ticket in Japan as \( J \) and in Switzerland as \( S \).
From the given information, we can set up two equations:
1. \( 3J + 2S = 77.89 \) (Cost of three tickets in Japan plus two tickets in Switzerland)
2. \( 3S + 2J = 74.01 \) (Cost of three tickets in Switzerland plus two tickets in Japan)
Now, we can solve this system of linear equations to find the values of \( J \) and \( S \).
Multiplying the first equation by 3 and the second equation by 2, we get:
1. \( 9J + 6S = 233.67 \)
2. \( 6S + 4J = 148.02 \)
Now, subtract the second equation from the first:
\[ (9J + 6S) - (6S + 4J) = 233.67 - 148.02 \]
Solving this, you get \( 5J = 85.65 \), so \( J = 17.13 \).
Now, substitute the value of \( J \) into either of the original equations to find \( S \). Let's use the first equation:
\[ 3(17.13) + 2S = 77.89 \]
Solving for \( S \), you get \( S \approx 13.81 \).
So, the average movie ticket cost in Japan (\( J \)) is approximately $17.13, and in Switzerland (\( S \)) is approximately $13.81.