SOLUTION: (1 point) A concert venue sold 2225 tickets one evening. Tickets cost $40.00 for a covered pavilion seat and $25.00 for a lawn seat. Total receipts were $70,250.00 . How many of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: (1 point) A concert venue sold 2225 tickets one evening. Tickets cost $40.00 for a covered pavilion seat and $25.00 for a lawn seat. Total receipts were $70,250.00 . How many of       Log On


   

Question 1049404: (1 point) A concert venue sold 2225 tickets one evening. Tickets cost $40.00 for a covered pavilion seat and $25.00 for a lawn seat. Total receipts were $70,250.00 . How many of each type of ticket were sold?
Lawn tickets:
Pavilion tickets:

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of covered pavillion seats sold
Let +b+ = number of lawn seat tickets sold
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(1) +a+%2B+b+=+2225+
(2) +40a+%2B+25b+=+70250+
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(2) +8a+%2B+5b+=+14050+
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +8a+%2B+5b+=+14050+
(1) +-5a+-+5b+=+-11125++
-------------------------
+3a+=+2925+
+a+=+975+
and
(1) +a+%2B+b+=+2225+
(1) +975+%2B+b+=+2225+
(1) +b+=+1250+
------------------------
975 of the covered pavillion seats were sold
1250 of the lawn seat tickets were sold
--------------------------------------
check:
(2) +40%2A975+%2B+25%2A1250+=+70250+
(2) +39000+%2B+31250+=+70250+
(2) +70250+=+70250+
OK