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If the company absorbed a $1000 loss on all the tickets, how much did an employee pay for a ticket?

This is the complete question:
The Alan company bought 80 tickets for a jazz concert. After giving away 20 to customers, the company sold the rest to employees at half of the purchase price. If the company absorbed a $1000 loss on all the tickets, how much did an employee pay for a ticket?
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2 Answers

  • Let p be the purchase price of a ticket.
  • The Alan company bought 80 tickets at a total cost of 80p
  • The company sold 60 tickets (the original 80 minus the 20 they gave away) at half price, so they made 60*(1/2)*p on the sale
  • The company lost $1000, which is the difference between what they spent on the tickets (the total cost) and what they made back from the sale
 
total cost - total made = total lost
80p - 60*(1/2)*p = $1000
80p - 30p = $1000
50p = $1000
p = $20
 
Since the purchase price p = $20, each employee spent (1/2)*$20 = $10 for a ticket.
Hi Abaline;
80-20=60 tickets sold
$1000=loss of purchase price
$2000=purchase price
$1000/60 tickets=$16.67/ticket