Question

Average movie prices in the United States are, in general, lower than in other countries. It would cost $ to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $. How much does an average movie ticket cost in each of these countries?

Answer 1

System of Equations

Let's set the variables:

x = average cost of movie tickets in Japan

y = average cost of movie tickets in Switzerland

We are given that 3 tickets in Japan plus 2 tickets in Switzerland cost $79.23. We also know 3 tickets in Switzerland and 2 tickets in Japan cost $74.72.

The system of equations is:

3x + 2y = 79.23 [1]

2x + 3y = 74.72 [2]

To solve the system we multiply [1] by -2 and [2] by 3:

-6x - 4y = -158.46

6x + 9y = 224.16

Adding both equations:

5y = 65.7

Dividing by 5:

y = 13.14

Solving [1] for x:

3x = 79.23 - 2y

Substituting:

3x = 79.23 - 2(13.14)

3x = 52.95

Dividing by 3:

x = 17.65

Answer:

In Japan average cost is $13.14

In Switzerland average cost is $17.65