SOLUTION: a theater has 15 seats, divided into balcony, main floor, and orchestra seating. Balcony seats sell for $1, main floor seats for $2, and orchestra seats for $3. If all seats were s

Question 1120201: a theater has 15 seats, divided into balcony, main floor, and orchestra seating. Balcony seats sell for $1, main floor seats for $2, and orchestra seats for $3. If all seats were sold, the total revenue to the theater is $24. There are 4 times as many balcony seats as there are orchestra seats. how many are there of each kind?
Answer by ikleyn(52765) (Show Source): You can put this solution on YOUR website!
.

Let x = #orchestra seats.


Then the number of balcony seats is 4x and the number of the main floor seats is 15 - (x+4x) = 15-5x.


The "money equation" is


1*(4x) + 3*x + 2*(15-5x) = 24    dollars.


Simplify and solve for x:


4x + 3x + 30 - 10x = 24,

-3x = 24-30 = -6  ====>  x =  = 2.


Answer.  2 orchestra seats;  4*2 = 8 balcony sears;  and  15-5x = 15-5*2 = 5 main floor seats.

Solved.

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The lesson to lear from this solution :

     This problem is for one unknown and one equation.

To see many other similar solved problems, look into the lesson
- Advanced word problems to solve using a single linear equation
in this site.

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