Question

Average movie prices in the United States are, in general, lower than in other countries. It would cost $80.50 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $76.85. How much does an average movie ticket cost in each of these countries?

Answer 1

Japan - $21.95

Switzerland - $7.33

Explanation:

Let the cost of movies in Japan be x and the cost of movies in Switzerland be y. We can write two equations that relate x to y. If we have two equations and two unknowns we can solve for x and y.

For the total cost of $80.5:

`80.5=3\cdot{x}+2\cdot{y}`

WE can write in terms of y:

`80.5/2-(3/2)\cdot{x}=y`

and substitute into: total of $76.85:

`76.85=2\cdot{x}+3\cdot{y}`

`76.85=2\cdot{x}+3\cdot{80.5/2-(3/2)\cdot{x}}`

solve for x

`76.85-3\cdot{80.5/2}=2\cdot{x}-3\cdot{(3/2)\cdot{x}}`

`-43.9=-2.5\cdot{x}`

`x=21.95`

then y is:

`y=7.33`