A charity raffle offers a first prize of $1,000,000, a second place prize of $100,000 and a third place prize of $10,000. A total of 500 000 tickets will be sold. What price should be charged for a ticket in order for the charity to make a 60% profit on this raffle?
To determine the price that should be charged for a ticket in order for the charity to make a 60% profit on this raffle, we need to understand the concept of profit and the formula to calculate it.
Profit is calculated as the difference between the revenue earned and the costs incurred. In this case, the revenue is the total amount collected from selling the tickets, and the costs are the cash prizes given out to the winners.
To calculate the revenue, we multiply the number of tickets sold by the price per ticket. In this case, 500,000 tickets will be sold, and we want to find the price per ticket.
The costs are the sum of the cash prizes given out to the winners. In this case, the first prize is $1,000,000, the second prize is $100,000, and the third prize is $10,000.
The profit is 60% of the revenue. We can calculate the profit using the formula:
Profit = Revenue * Percentage Profit / 100
Let's break it down step by step:
1. Calculate the total costs:
Total costs = First prize + Second prize + Third prize
Total costs = $1,000,000 + $100,000 + $10,000
2. Calculate the target revenue:
Profit = Revenue * Percentage Profit / 100
Profit = (Revenue - Total costs) * 60 / 100
Revenue - Total costs = Profit * 100 / 60
Revenue = Total costs + (Profit * 100 / 60)
Revenue = Total costs + (Profit * 5 / 3)
3. Calculate the price per ticket:
Price per ticket = Revenue / Number of tickets sold
Price per ticket = (Total costs + (Profit * 5 / 3)) / Number of tickets sold
Now we can substitute the values into the formula to find the price per ticket:
Price per ticket = ($1,000,000 + $100,000 + $10,000 + (Profit * 5 / 3)) / 500,000
By plugging in the values for Profit, Total costs, and Number of tickets sold, you can calculate the price per ticket needed for the charity to make a 60% profit on this raffle.