Average movie prices in United States are, in general, lower than in other countries. It would cost $78.62 to buy three tickets in Japan plus two tickets in Switzerland. Thee tickets in Switzerland plus two tickets in Japan would cost $75.33. How much does an average movie ticket cost in each of these countries?

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absor201 absor201 · Answer 1 · 2019-11-29T14:58:37+01:00

An average movie ticket costs $17.04 in Japan and $13.75 in Switzerland.

Step-by-step explanation:

Let,

Japan's movie tickets = x

Switzerland's movie tickets = y

According to given statement;

3x+2y=78.62 Eqn 1

2x+3y=75.33 Eqn 2

Multiplying Eqn 1 by 2;

[tex]2(3x+2y=78.62)\\6x+4y=157.24\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 3;

[tex]3(2x+3y=75.33)\\6x+9y=225.99\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 3 from Eqn 4

[tex](6x+9y)-(6x+4y)=225.99-157.24\\6x+9y-6x-4y=68.75\\5y=68.75[/tex]

Dividing both sides by 5;

[tex]\frac{5y}{5}=\frac{68.75}{5}\\y=13.75[/tex]

Putting y=13.75 in Eqn 1

[tex]3x+2(13.75)=78.62\\3x+27.50=78.62\\3x=78.62-27.50\\3x=51.12\\[/tex]

Dividing both sides by 3;

[tex]\frac{3x}{3}=\frac{51.12}{3}\\x=17.04[/tex]

An average movie ticket costs $17.04 in Japan and $13.75 in Switzerland.

Keywords: linear equations, subtraction

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