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 find 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 calculate the total cost and the desired profit.
First, let's calculate the total cost:
The charity will need to give out $1,000,000 for the first prize, $100,000 for the second prize, and $10,000 for the third prize. Therefore, the total cost is $1,000,000 + $100,000 + $10,000 = $1,110,000.
To make a 60% profit on this raffle, the charity wants to earn an additional 60% of the total cost.
Profit = 60% of Total Cost
Profit = 60% of $1,110,000
To find 60% of $1,110,000, we multiply it by 0.6:
Profit = $1,110,000 * 0.6
Profit = $666,000
So, the desired profit for the charity is $666,000.
Now, let's calculate the revenue needed for this profit:
Revenue = Total Cost + Profit
Revenue = $1,110,000 + $666,000
Revenue = $1,776,000
Since the revenue is the amount the charity expects to receive from selling tickets, it should be equal to the number of tickets sold multiplied by the price of each ticket:
Revenue = Price x Number of Tickets Sold
$1,776,000 = Price x 500,000
To find the price per ticket, divide the revenue by the number of tickets sold:
Price = $1,776,000 / 500,000
Price = $3.552
Therefore, the price that should be charged for a ticket is $3.552 in order for the charity to make a 60% profit on this raffle.