Question

A box office sells balcony seats, ground-level seats, and VIP passes for shows on tour. The table shows the numbers of each type of ticket sold and the revenues for the first three shows of a tour. What is the price of each type of ticket?

Answer 1

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 = $$x$

Let the price of one Ground level seat = $$y$

Let the price of one VIP seat = $$z$

As per the given table:

$135x+280y+29z=37170 ....... (1)\\150x+270y+58z=42240 ....... (2)\\130x+265y+29z=35570 ....... (3)$

Multiplying (1) with 2 and subtracting (2) from it:

$120x+290y=32100 \\12x+29y=3210..... (4)$

Subtracting (3) from (1):

$5x+15y=1600\\x+3y=320 ....... (5)$

Multiply equation (5) with 12 and subtracting (4) from it:

$7y=630\\\Rightarrow y =\bold{90}$

By equation (5), putting value of $y$:

$x=\bold{50}$

By equation (1), putting the values of $x, y:$

$135\times 50+280\times 90+29z=37170\\\Rightarrow 29z=37170-31950\\\Rightarrow 29z=5220\\\Rightarrow z =\bold{180}$

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