SOLUTION: Tickets for a high school dance cost $1.00 each if purchased in advance of the dance, but $1.50 each if bought at the door. If 100 tickets were sold and $120 was collected, how man

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Question 725854: Tickets for a high school dance cost $1.00 each if purchased in advance of the dance, but $1.50 each if bought at the door. If 100 tickets were sold and $120 was collected, how many tickets were sold in advance and how many we're sold at the door?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of tickets sold in advance
Let +b+ = number sold at the door
given:
(1) +a+%2B+b+=+100+
(2) +1%2Aa+%2B+1.5%2Ab+=+120+
-----------------------
(2) +10a+%2B+15b+=+1200+
(2) +2a+%2B+3b+=+240+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2a+%2B+3b+=+240+
(1) +-2a+-+2b+=+-200+
+b+=+40+
and, since
(1) +a+%2B+b+=+100+
(1) +a+%2B+40+=+100+
(1) +a+=+60+
60 tickets were sold in advance
40 tickets were sold at the door
check:
(2) +1%2Aa+%2B+1.5%2Ab+=+120+
(2) +1%2A60+%2B+1.5%2A40+=+120+
(2) +60+%2B+60+=+120+
(2) +120+=+120+
OK