In theatre 2

A ticket for the balcony costs x CZK, and for the auditorium costs y CZK. For the afternoon performance, they sold 98 tickets for the balcony and 186 tickets for the auditorium, earning a total of 10970 CZK. For the evening performance, they sold 127 balcony tickets and 155 auditorium tickets, earning a total of 11,635 CZK. How much did a balcony ticket cost and how much did a theater ticket cost?

Correct answer:

x =  55
y =  30

Step-by-step explanation:


98x+186y = 10970
127x+155y = 11635

98·x+186·y = 10970
127·x+155·y = 11635

98x+186y = 10970
127x+155y = 11635

Pivot: Row 1 ↔ Row 2
127x+155y = 11635
98x+186y = 10970

Row 2 - 98/127 · Row 1 → Row 2
127x+155y = 11635
66.39y = 1991.81


y = 1991.81102362/66.39370079 = 30
x = 11635-155y/127 = 11635-155 · 30/127 = 55

x = 55
y = 30

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