SOLUTION: For the opening night at the Opera House, a total of 1000 tickets were sold. Front orchestra seats cost $80 apiece, rear orchestra seats cost $60 apiece, and front balcony seats

Question 1144535: For the opening night at the Opera House, a total of 1000 tickets were
sold. Front orchestra seats cost $80 apiece, rear orchestra seats cost $60
apiece, and front balcony seats cost $50 apiece. The combined number of
tickets sold for the front orchestra and rear orchestra exceeded twice the
number of front balcony tickets sold by 400. The total receipts for the
performance were $62,800. Determine how many tickets of each type were
sold?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
For the opening night at the Opera House, a total of 1000 tickets were sold.
Front orchestra seats cost $80 apiece, rear orchestra seats cost $60 apiece, and front balcony seats cost $50 apiece.
The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by 400.
The total receipts for the performance were $62,800.
Determine how many tickets of each type were sold?
:
let a = no. of front orches seats
let b = no. of rear orches seats
let c = no. of front balcony seats
:
Write an equation for each statement
:
"For the opening night at the Opera House, a total of 1000 tickets were sold."
a + b + c = 1000
" The total receipts for the performance were $62,800. "
80a + 60b + 50c = 62800
:
"The combined number of tickets sold for the front orchestra and rear orchestra exceeded twice the number of front balcony tickets sold by 400. "
a + b = 2c + 400
a + b - 2c = 400
:
use elimination on these two equation
a + b + c = 1000
a + b - 2c = 400
------------------subtraction eliminates a & b, find c
0 + 0 + 3c = 600
c = 600/3
c = 200 front balcony seats
:
form two 2 unknown equations with c = 200
a + b + 200 = 1000
a + b = 800
and
80a + 60b + 50(200) = 62500
80a + 60b + 10000 = 62500
80a + 60b = 52800
multiply the 1st equation by 60, subtract from the above equation
80a + 60b = 52800
60a + 60b = 48000
------------------- subtraction eliminates b, find a
20a + 0 = 4800
a = 4800/20
a = 240 front orches seats
Then
240 + b + 200 = 1000
b = 1000 - 440
b = 560 rear orches seats
:
:
Check this on your calc
80(240) + 60(560) + 50(200) = 62800

RELATED QUESTIONS
For the opening night at the Opera House, a total of 1000 tickets were sold. Front... (answered by solver91311,ikleyn)

At a Performing Arts Center, seats in the orchestra section cost $18 and seats in the... (answered by math_helper)

A theater has 80 seats. On opening night, they sold out, selling adult tickets for $12... (answered by josmiceli)

t the opening night of the phantom of the opera, two different types of souvenirs were... (answered by solver91311)

Orchestra seats for a Symphony performance cost $6 more than balcony seats. If 400... (answered by ikleyn)

A ballet company sells 540 tickets for its upcoming performance of Swan Lake. Tickets for (answered by Shin123,MathTherapy)

El Segundo High School put on their annual musical. the students sold 650 tickets for a... (answered by misscrt,MathLover1,stanbon)

Please help I cant figure out how to set this up: Tickets to a theater cost $35 each for (answered by ewatrrr)

On the opening night of a play at a local theater, 992 tickets were sold for a... (answered by josgarithmetic,MathTherapy)