R&N is a new candy with magical (yet mathematical) properties. Not all candies are the same size. When removing the largest R&N from a new bag, the bag becomes 1/2 full; removing the second largest makes the bg 1/3 full; removing the third largest makes it 1/4 full, and so on. Dr. Lutinski opens a new bag on Monday and eats the largest candy. On Tuesday he eats the next few largest, leaving 5/14 fewer than on Monday. How many did Dr. Lutinski eat?
To solve this problem, we need to establish a mathematical relationship between the number of candies eaten by Dr. Lutinski and the number of candies in the bag.
Let's assume that the total number of candies in the bag initially is "x."
According to the given information, removing the largest candy leaves the bag 1/2 full. This means that after eating the largest candy, there are (1/2)x candies left in the bag.
Similarly, removing the second largest candy leaves the bag 1/3 full, so there will be (1/3)x candies left after eating the second largest candy.
Continuing this pattern, after eating the third largest, there will be (1/4)x candies left, and so on.
Now, let's analyze the information given about the bag on Tuesday. It states that there are 5/14 fewer candies than on Monday. So, we can express the number of candies left on Tuesday as (x - 5/14x).
Now, let's equate the number of candies left on Tuesday with the earlier derived expression for the number of candies left after eating the largest, second largest, etc.
(x - 5/14x) = (1/2)x - (1/3)x - (1/4)x - ...
Simplifying the equation, we get:
13x/14 = (1/2)x - (1/3)x - (1/4)x - ...
Now, solving for x, we can find the total number of candies initially in the bag. Subtracting the number of candies left on Tuesday from the initial total will give us the number of candies eaten by Dr. Lutinski.
After finding x, subtract (x - 5/14x) to get the number of candies eaten by Dr. Lutinski.
Note: This problem involves solving a series of equations and might require some algebraic manipulation.