Question

Average movie prices in the United States​ are, in​ general, lower than in other countries. It would cost
​$81.0881.08
to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost
​$76.9776.97.
How much does an average movie ticket cost in each of these​ countries?

Answer 1

Answer on Question #61308 – Math – Algebra

Question

Average movie prices in the United States are, in general, lower than in other countries.

It would cost

$81.08

to buy three tickets in Japan plus two tickets in Switzerland.

Three tickets in Switzerland plus two tickets in Japan would cost

$76.97.

How much does an average movie ticket cost in each of these countries?

Solution

Let $x$ be the cost (in dollars) of a ticket in Japan and $y$ be the cost (in dollars) of a ticket in Switzerland.

Given

$$\left\{ \begin{array}{l} 3x + 2y = 81.08 \\ 2x + 3y = 76.97 \end{array} \right.$$

Multiplying the first equation by 3 and the second equation by 2

$$\left\{ \begin{array}{l} 9x + 6y = 243.24 \\ 4x + 6y = 153.94 \end{array} \right.$$

Subtracting the second equation from the first one

$$9x + 6y - 4x - 6y = 243.24 - 153.94.$$

Simplifying

$$5x = 89.3.$$

Dividing both sides by 5

$$x = \frac{89.3}{5},$$

$x = 17.86$ is the cost of a ticket in Japan.

Expressing $y$ from the first equation of the system and substituting for $x = 17.86$

$$y = \frac{81.08 - 3x}{2},$$ $$y = \frac{81.08 - 3 \cdot 17.86}{2},$$

$y = 13.75$ is the cost of a ticket in Switzerland.

**Answer:**

Ticket in Japan costs $17.86.

Ticket in Switzerland costs $13.75.

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