Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.92 to buy thre tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $75.18
much does an average movie ticket cost in each of these countries?
Let's assume the average movie ticket price in the United States is x.
According to the given information:
3 tickets in Japan + 2 tickets in Switzerland = $78.92
2 tickets in Japan + 3 tickets in Switzerland = $75.18
From these equations, we can create a system of equations:
3x + 2y = $78.92 ----(1)
2x + 3y = $75.18 ----(2)
To solve this system, we can use the method of substitution or elimination. Here, we will use the method of elimination:
Multiply equation (1) by 2 and equation (2) by 3 to eliminate the x-term:
6x + 4y = $157.84 ----(3)
6x + 9y = $225.54 ----(4)
Now, subtract equation (3) from equation (4) to eliminate the x-term:
(6x + 9y) - (6x + 4y) = $225.54 - $157.84
5y = $67.70
y = $67.70 / 5
y ≈ $13.54
Substitute the value of y into equation (1) to solve for x:
3x + 2(13.54) = $78.92
3x + 27.08 = $78.92
3x = $78.92 - $27.08
3x = $51.84
x = $51.84 / 3
x ≈ $17.28
Therefore, the average movie ticket price in Japan is approximately $17.28, and in Switzerland, it is approximately $13.54.