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Sagot :
If "J" is the average price in Japan and "S" is the average price is "S", then since we are told that three tickets in Japan plus two tickets in Switzerland cost $77.94 we have the following relationship:
[tex]3J+2S=77.94,\text{ (1)}[/tex]We are also told that three tickets in Switzerland plus two tickets in Japan would cost $73.86. This gives us the following equation:
[tex]2J+3S=73.86,(2)[/tex]We get two equations with two variables. To solve this system we will multiply equation (1) by -2:
[tex]-6J-4S=-155.88,(3)[/tex]Now we multiply equation (2) by 3:
[tex]6J+9S=221.58,(4)[/tex]Now we will add equation (3) and equation (4):
[tex]-6J-4S+6J+9S=-155.88+221.58[/tex]Now we add like terms;
[tex]5S=65.7[/tex]Dividing both sides by 5:
[tex]S=\frac{65.7}{5}=13.14[/tex]Now we replace the value of S in equation (1):
[tex]3J+2(13.14)=77.94[/tex]Solving the operation:
[tex]3J+26.28=77.94[/tex]Subtracting 26.28 to both sides:
[tex]\begin{gathered} 3J=77.94-26.28 \\ 3J=51.66 \end{gathered}[/tex]Dividing both sides by 3:
[tex]J=\frac{51.66}{3}=17.22[/tex]Therefore, the average in Japan is $17.22 and the average in Switzerland is $13.14.
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