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 find out how many candies Dr. Lutinski ate, we need to work backward from the information given.
Let's assume there were a total of "x" candies in the new bag that Dr. Lutinski opened on Monday.
According to the problem, removing the largest candy makes the bag 1/2 full. So, after the largest candy was removed, there would be x/2 candies left in the bag.
Removing the second largest candy makes the bag 1/3 full. So, after the second largest candy is taken out, there would be (x/2)/3 candies left in the bag, which simplifies to x/6.
Following this pattern, removing the third largest candy makes the bag 1/4 full. So, after the third largest candy is eaten, there would be (x/6)/4 candies left in the bag, which simplifies to x/24.
By continuing this process, we can determine that on Tuesday, there were 5/14 fewer candies than on Monday. Therefore, the equation becomes:
x - (x/24) = x - (5/14)
Simplifying this equation gives us:
x/24 = 5/14
To solve for x, we'll cross-multiply and solve for x:
14x = 5 * 24
14x = 120
x = 120/14
x ≈ 8.57
So, there were approximately 8.57 candies in the bag that Dr. Lutinski opened on Monday.
Since we cannot have a fraction of a candy, we assume that there were 9 candies in the bag. Therefore, Dr. Lutinski ate 9 - (5/14) = 8 candies.