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 will set up a mathematical equation based on the information given.
Let's assume that the original number of candies in the bag is "x".
According to the information given, when Dr. Lutinski removes the largest candy from the bag, the bag becomes 1/2 full. This means that there are (1/2) * x candies remaining in the bag.
Similarly, when Dr. Lutinski removes the second largest candy, the bag becomes 1/3 full. So, (1/3) * x candies remain in the bag.
We can continue this pattern for each subsequent removal of candies. Based on the information given, we can set up the following equation:
x - x*(1/2) - x*(1/3) - x*(1/4) - ... = 5/14
Simplifying the equation, we have:
14x - 7x - 4x - 3x - ... = 5
Adding the negative fractions, we get:
14x - (7x + 4x + 3x + ...) = 5
Now, let's simplify the right side of the equation:
14x - (7x + 4x + 3x + ...) = 5
14x - (14x - 5) = 5
14x - 14x + 5 = 5
5 = 5
Since both sides of the equation are equal, it means that the equation is true regardless of the value of "x". Therefore, "x" cancels out from the equation.
This implies that Dr. Lutinski did not eat any candies from the bag. The equation 14x - (7x + 4x + 3x + ...) = 5 holds true even without subtracting any candies eaten by the doctor.
So, the answer is that Dr. Lutinski did not eat any candies from the bag.