Final answer:
The minimum number of in-person tickets that must be sold for the group to meet their goal of $4,000 in sales, after selling 240 tickets online, is 154 tickets.
Step-by-step explanation:
The minimum number of tickets that must be sold in person for the group sponsoring the Renaissance Faire to meet their goal of $4,000 can be found through a simple algebraic equation. We already know that 240 passes were sold online at $9 each. Therefore, the total revenue from online pass sales is 240 passes × $9/pass, which equals $2,160.
The group's goal is to make at least $4,000. To find out how much more money is needed to reach this goal, we subtract the revenue from online sales from the total goal: $4,000 - $2,160 = $1,840.
Since in-person tickets are sold at $12 each, we divide the needed revenue of $1,840 by $12 to find out the minimum number of in-person tickets that must be sold: $1,840 ÷ $12/ticket = 153.33. Since we cannot sell a fraction of a ticket, we round up to the next whole number, which gives us a minimum of 154 in-person tickets needed to meet the sales goal. To find the minimum number of tickets that must be sold in person in order for the group to meet its goal, we need to calculate the total revenue from both online and in-person ticket sales.
Given that 240 passes were sold online, the revenue from online sales would be $9 multiplied by 240, which is $2,160.
To reach a minimum goal of $4,000, the revenue from in-person ticket sales should be at least $4,000 - $2,160, which is $1,840.
Since each in-person ticket is priced at $12, we can divide $1,840 by $12 to find the minimum number of tickets that must be sold in person. The answer is 153.33, but since we can't sell a fractional number of tickets, the minimum number of tickets that must be sold in person is 154.