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
Algebra ->
College
-> Linear Algebra
-> 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
Log On
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(52756) (Show Source):
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.
