SOLUTION: PROBLEM: THE FORREST THEATER CAN SEAT A TOTAL OF 360 PEOPLE. THEY TAKE IN $15,150 WHEN EVERY SEAT IS SOLD FOR A PERFORMANCE. IF THE ORCHESTRA SECTION TICKETS COST $45 AND THE BALC

Question 136863: PROBLEM:
THE FORREST THEATER CAN SEAT A TOTAL OF 360 PEOPLE. THEY TAKE IN $15,150 WHEN EVERY SEAT IS SOLD FOR A PERFORMANCE. IF THE ORCHESTRA SECTION TICKETS COST $45 AND THE BALCONY TICKETS COST $35, FIND THE NUMBER OF SEATS IN AVAILABLE IN EACH SECTION.
PLEASE HELP I DON'T EVEN KNOW WHERE TO BEGIN??? THANKS
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=number of seats in the orchestra section
And y=number of seats in the balcony section
Now we are told the following:
x+y=360-----------------------------------------------eq1
and ($ understood)
45x+35y=15,150-----------------------------------------eq2
eq2 reduces to (divide each term by 5):
9x+7y=3030-------------------------------------------------eq2a
from eq1, we see that x=360-y, substitute this into eq2a:
9(360-y)+7y=3030 get rid of parens
3240-9y+7y=3030 subtract 3240 from each side
3240-3240-9y+7y=3030-3240 collect like terms
-2y=-210 divide both sides by -2
y=105------------------------------------number of seats in the Balcony sect.
Substitute y=105 into eq1:
x+105=360 subtract 105 from each side
x=255------------------------number of orchestra seats
CK
105+255=360
360=360
and
45*255+35*105=15,150
11,475+3,675=15,150
15,150=15,150
Hope this helps----ptaylor

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