Question

A movie theater earned $3,600 in sold-out ticket sales for the premiere of a new movie. VIP tickets cost $20 per person and regular admission tickets cost $8 per person. If the number of regular admission tickets sold was twice the number of VIP tickets sold, what was the total number of seats in the theater?

Answer 1

There are 300 seats in the theater.

Step-by-step explanation:

Given,

Cost of one VIP ticket = $20

Cost of one regular ticket = $8

Worth of sold out tickets = $3600

Let,

x represent the number of VIP tickets sold

y represent the number of regular tickets sold

20x+8y=3600     Eqn 1

y = 2x                   Eqn 2

Putting value of y from Eqn 2 in Eqn 1

$20x+8(2x)=3600\\20x+16x=3600\\36x=3600$

Dividing both sides by 36

$\frac{36x}{36}=\frac{3600}{36}\\x=100$

Putting x=100 in Eqn 2

$y=2(100)\\y=200$

Total = x+y = 100+200 = 300

There are 300 seats in the theater.

Keywords: linear equation, substitution method

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