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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