A box containing Munchkins contains chocolate and glazed donut holes. If Gloria ate 2 chocolate Munchkins, then 1/11 of the remaining Munchkins would be chocolate. If Gloria added 4 glazed Munchkins to the box, 1/7 of the Munchkins would be chocolate. How many Munchkins are in the original box?
If Gloria added 4 glazed Munchkins to the box, the proportion of chocolate increased from 1/11 to 1/7?
You will get negative numbers as answers.
Below, I assume you have switched the two proportions between 1/11 and 1/7.
If my guess proves to be wrong, the solution method remains the same.
G = glazed
C = chocolate
7(C-2) = G + C-2
11(C-2) = G+4 + C-2
or
6C-G =12
10C-G = 24
Solve for G and C to get
G=6, C=3
To solve this problem, let's break it down step by step.
Let's assume there are X total Munchkins in the original box. We'll use this variable to find the answer.
We know from the problem that if Gloria ate 2 chocolate Munchkins, then 1/11 of the remaining Munchkins would be chocolate. So initially, there were X - 2 Munchkins left in the box after Gloria ate the 2 chocolate Munchkins.
According to the information given, we can set up the equation:
(1/11)(X - 2) = the number of chocolate Munchkins in the remaining box
Now, let's move on to the next piece of information. If Gloria added 4 glazed Munchkins to the box, 1/7 of the Munchkins would be chocolate. So the new total number of Munchkins in the box would be X + 4.
Using this information, we can set up the equation:
(1/7)(X + 4) = the number of chocolate Munchkins in the new box
Now we have two equations:
(1/11)(X - 2) = (1/7)(X + 4)
To solve this, we can multiply both sides of the equation by 77 (the least common multiple of 11 and 7) to get rid of the denominators:
7(X - 2) = 11(X + 4)
Simplify both sides of the equation:
7X - 14 = 11X + 44
Combine like terms:
4X = 58
Dividing both sides of the equation by 4:
X = 58/4
X = 14.5
Since we cannot have half a Munchkin, it means our initial assumption was incorrect. So, we need to adjust and try again.
Let's assume there are Y total Munchkins in the original box. We'll use this new variable to find the correct answer.
Proceeding in the same manner, we can rewrite our equations:
(1/11)(Y - 2) = (1/7)(Y + 4)
Multiply both sides by 77:
7(Y - 2) = 11(Y + 4)
Simplify and combine like terms:
7Y - 14 = 11Y + 44
Subtract 11Y from both sides and add 14 to both sides to isolate Y:
7Y - 11Y = 44 + 14
-4Y = 58
Dividing both sides by -4:
Y = -58/4
Y = -14.5
Since we cannot have a negative number of Munchkins, this result is not valid either.
Therefore, there is no solution to this problem with the given information.