Average movie prices in the United States are, in general, lower than in other countries. It would cost $81.43 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $77.37. How much does an average movie ticket cost in each of these countries?
Let's assume the cost of one movie ticket in the US is x.
Based on the given information:
3 tickets in Japan cost $81.43. Hence, the cost of one ticket in Japan is 81.43/3 = $27.14.
2 tickets in Switzerland cost $81.43 - (3 * x) = $81.43 - 3x.
Therefore, the cost of one ticket in Switzerland is (81.43 - 3x)/2.
Also, 3 tickets in Switzerland cost $77.37. Hence, the cost of one ticket in Switzerland is 77.37/3 = $25.79.
We can equate the two expressions for the cost of one ticket in Switzerland:
(81.43 - 3x)/2 = $25.79.
Multiplying both sides by 2, we get:
81.43 - 3x = 2 * 25.79
81.43 - 3x = 51.58
-3x = 51.58 - 81.43
-3x = -29.85
x = -29.85 / -3
x = $9.95
Therefore, the average movie ticket price in the United States is $9.95.
Substituting the value of x into the expression for the cost of one ticket in Japan, we get:
Cost of one ticket in Japan = 81.43/3 = $27.14.
Substituting the value of x into the expression for the cost of one ticket in Switzerland, we get:
Cost of one ticket in Switzerland = (81.43 - 3*x)/2 = (81.43 - 3 * 9.95)/2 = $15.24.
So, the average movie ticket prices in each country are as follows:
United States: $9.95
Japan: $27.14
Switzerland: $15.24