Another variety of R&Ns has a different set of magical (yet mathematical) properties. Remove exactly 4 candies and 1 additional candy appears in the bag. According to the package, a bag contains 50 candies. What is the maximum number of canies that this variety of R&Ns will yield?
To find the maximum number of candies this variety of R&Ns will yield, we'll need to determine the number of candies that can be removed to create additional candies multiple times until it is no longer possible.
Let's start by removing 4 candies from the bag. According to the properties mentioned, 1 additional candy will appear in the bag. This means that after removing 4 candies, we will have a net gain of 1 candy.
Now, let's consider the process again. We'll remove another 4 candies from the bag, resulting in 1 additional candy appearing.
We can repeat this process until we are unable to remove another 4 candies.
Since each time we remove 4 candies we gain 1 additional candy, we can calculate the maximum number of times we can remove 4 candies:
50 (initial candies) ÷ 4 (candies removed each time) = 12.5
Since we cannot remove a fraction of a candy, we need to round down to the nearest whole number. Therefore, we can remove 4 candies a maximum of 12 times.
Now, let's calculate the maximum number of candies yielded:
12 (rounds of removing 4 candies) × 1 (additional candy per round) = 12 additional candies
Finally, we need to add this to the initial number of candies:
50 (initial candies) + 12 (additional candies) = 62
Therefore, the maximum number of candies this variety of R&Ns will yield is 62.