Answer:
The price of one Balcony seat = $50
The price of one Ground level seat = $90
The price of one VIP seat = $180
Step-by-step explanation:
Let the price of one Balcony seat = $[tex]x[/tex]
Let the price of one Ground level seat = $[tex]y[/tex]
Let the price of one VIP seat = $[tex]z[/tex]
As per the given table:
[tex]135x+280y+29z=37170 ....... (1)\\150x+270y+58z=42240 ....... (2)\\130x+265y+29z=35570 ....... (3)[/tex]
Multiplying (1) with 2 and subtracting (2) from it:
[tex]120x+290y=32100 \\12x+29y=3210..... (4)[/tex]
Subtracting (3) from (1):
[tex]5x+15y=1600\\x+3y=320 ....... (5)[/tex]
Multiply equation (5) with 12 and subtracting (4) from it:
[tex]7y=630\\\Rightarrow y =\bold{90}[/tex]
By equation (5), putting value of [tex]y[/tex]:
[tex]x=\bold{50}[/tex]
By equation (1), putting the values of [tex]x, y:[/tex]
[tex]135\times 50+280\times 90+29z=37170\\\Rightarrow 29z=37170-31950\\\Rightarrow 29z=5220\\\Rightarrow z =\bold{180}[/tex]
Therefore, the answers are:
The price of one Balcony seat = $50
The price of one Ground level seat = $90
The price of one VIP seat = $180
