SOLUTION: A theater has 500 balcony seats and 1800 main level seats. If tickets for balcony seats will cost $15 less than tickets for main level seats, what should the prices be for each typ

Question 952779: A theater has 500 balcony seats and 1800 main level seats. If tickets for balcony seats will cost $15 less than tickets for main level seats, what should the prices be for each type of ticket so that total revenue from a sellout performance will be $33,840?
Found 2 solutions by MathLover1, macston:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
A theater has balcony seats and main level seats.

if all tickets sold:
and , the revenue will be:

If tickets for balcony seats will cost $ less than tickets for main level seats , then

what should the prices be for each type of ticket so that total revenue from a sellout performance will be $:
$ ......solve for
$
$
$
$
$
$ ->price be for ticket for main level seats
then, will be
$
$->->price be for ticket for balcony seats

check the revenue:
$
$
$
$..round it
$

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
B=balcony seats=M-$15; M=main level seats
500B+1800M=$33840 Substitute for B.
500(M-$15)+1800M=$33840
500M-$7500+1800M=$33840 Add $7500 to each side.
2300M=$41340
M=$17.97 ANSWER 1: Mail level seats cost $17.97
B=$17.97-$15=$2.97 ANSWER 2: Balcony seats cost $2.97
CHECK:
500($2.97)+1800($17.97)=$33840
$1485+$32346=$33840
$33831=$33840 (Difference due to rounding down 0.4 of a cent per ticket)

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