Average movie ticket cost in Japan = $17.23
Average movie ticket cost in Switzerland = $ 13.52
Step-by-step explanation:
Let <em>x</em> be the cost of movie ticket in Japan and <em><u>y</u></em> be the cost of movie ticket in Switzerland.
Given 3 ticket in Japan + 2 tickets in Switzerland = $78.73
⇒ 3<em>x</em> + 2<em>y</em> = 78.73 – – – – (1)
Given 3 ticket in Switzerland + 2 tickets in Japan = $75.02
⇒ 3<em>y</em> + 2<em>x</em> = 75.02
⇒ 2<em>x</em> + 3<em>y</em> = 75.02– – – – – (2)
Now, to solve (1) and (2), we multiply equation (1) by 2 and equation (2) by 3.
(1) × 2 ⇒ 6<em>x</em> + 4<em>y</em> = 157.46 – – – – (3)
(2) × 3 ⇒ 6<em>x</em> + 9<em>y</em> = 225.06 – – – – (4)
Subtract (3) from (4), we get
6<em>x </em>+ 9<em>y</em> – (6<em>x</em> + 4<em>y</em>)= 225.06 – 157.46
⇒ 6<em>x</em> + 9<em>y</em> – 6<em>x </em>– 4<em>y</em>= 67.6
⇒ 5<em>y</em> = 67.6
⇒ <em>y</em> = 13.52
Now substitute <em>y</em> = 13.52 in equation (1), we get,
(1) ⇒ 3<em>x</em> + 2(13.52) = 78.73
⇒ 3<em>x</em> = 78.73 – 27.04
⇒ <em>x</em> = 27.23
Hence, Average movie ticket cost in Japan is $27.23
Average movie ticket cost in Switzerland is $ 13.52.
