A popular performer is scheduled to appear at a major city. The promoter is deciding between two venues, the larger of which costs $20,000 to rent and the smaller of which costs $12,000 to rent. Ticket prices for the smaller venue are $20, but the promoter is unsure what to charge per ticket for the larger venue. If exactly 1000 customers arrive, what percentage change in ticket prices would make the profit at the large venue identical to that of the smaller venue?

40%

Explanation:

Cost to rent smaller venue = $12,000

Price per ticket for smaller venue = $20

Revenue generated for 1000 customers that arrived = 1000 * $20 = $20,000

Profit = revenue - cost = $20,000 - $12,000 = $8,000

For the larger venue to realize the same profit as the smaller venue ($8,000), the price per ticket must be $28 so it can generate a revenue of $28,000 (1000*$28) for the 1000 customers that arrived

Cost to rent larger venue = $20,000

Profit = revenue - cost = $28,000 - $20,000 = $8,000

% change in ticket prices = (price per ticket for larger venue - price per ticket for smaller venue) / price per ticket for smaller venue * 100 = ($28 - $20) / $20 * 100 = $8/$20 * 100 = 40%