Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.10 to buy three tickets in Japan plus two tickets in Switzerla Three tickets in Switzerland plus two tickets in Japan would cost $73.80. 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 + 2 tickets in Switzerland = $78.10
So, 3x + 2y = $78.10 ..........(1)
Also,
3 tickets in Switzerland + 2 tickets in Japan = $73.80
So, 3y + 2x = $73.80 ..........(2)
We now have a system of equations to solve (1) and (2).
Multiplying equation (1) by 2 and equation (2) by 3, we get:
6x + 4y = $156.20
9y + 6x = $221.40
Subtracting equation (1) from equation (2), we have:
6y + 2x = $43.20 .......(3)
From equations (1) and (3), we can now solve for x and y.
Subtracting equation (1) from equation (3), we get:
4y = $35
Dividing both sides by 4, we get:
y = $35/4
y = $8.75
Substituting the value of y in equation (1), we have:
3x + 2($8.75) = $78.10
3x + $17.50 = $78.10
3x = $78.10 - $17.50
3x = $60.60
Dividing both sides by 3, we get:
x = $60.60/3
x = $20.20
Therefore, the average price of a movie ticket in Japan is $8.75 and in Switzerland is $20.20.