BOX-OFFICE RECEIPTS 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.
BOX-OFFICE RECEIPTS 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.
Solution Summary: The author calculates the number of tickets sold for front, rear, and balcony seats, using the Gauss-Jordan elimination method.
BOX-OFFICE RECEIPTS 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.
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