SOLUTION: you belong to a school organization that is trying to raise money for its annual trip to new york city. the organization decides to hold a concert at a local site that can accomada

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Question 521515: you belong to a school organization that is trying to raise money for its annual trip to new york city. the organization decides to hold a concert at a local site that can accomadate 1500 people. it will cost the organization $1200 to rent the hall and provide security. the band wants $3000 but you get them to agree to a price of $2000 plus 20% of the cost of each ticket sold with a limit of $5000. you are pretty sure the band will attract at least 800 people. if you want the breakeven point to be 800 tickets sold what must be the price of the ticket?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The break even point would be where profit = 0
Let P = profit
Let x = the price of a ticket
given:
+P+=+800x+-+%28+1200++%2B+2000+%2B+.2%2A800x+%29+
+0+=+800x+-+%28+1200++%2B+2000+%2B+.2%2A800x+%29+
+800x+=+3200+%2B+.2%2A800x+
+800x+-+.2%2A800x+=+3200+
+.8%2A800x+=+3200+
+x+=+3200+%2F+640+
+x+=+5+
$5 should be the price of ticket
Also, the agreement was
+2000+%2B+.2%2A800x+%3C=+5000+
+2000+%2B+.2%2A800%2A5+%3C=+5000+
+2000+%2B+800+%3C=+5000+
+2800+%3C=+5000+
OK
check:
+0+=+800x+-+%28+1200++%2B+2000+%2B+.2%2A800x+%29+
+0+=+800%2A5+-+%28+1200++%2B+2000+%2B+.2%2A800%2A5+%29+
+0+=+4000+-+1200+-+2800+
+0+=+0+
OK