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?
See:
http://www.jiskha.com/display.cgi?id=1306204585
To solve this problem, let's assume the original number of Munchkins in the box is "x."
According to the problem, if Gloria ate 2 chocolate Munchkins, then 1/11 of the remaining Munchkins would be chocolate. This means that (x - 2) * (1/11) = the number of chocolate Munchkins. Simplifying this equation, we get (x - 2)/11 = the number of chocolate Munchkins.
Next, the problem states that if Gloria added 4 glazed Munchkins to the box, 1/7 of the Munchkins would be chocolate. This means that (x + 4) * (1/7) = the number of chocolate Munchkins. Simplifying this equation, we get (x + 4)/7 = the number of chocolate Munchkins.
Now we can set up an equation for the number of chocolate Munchkins based on the two statements:
(x - 2)/11 = (x + 4)/7
To solve this equation, we will cross-multiply and then solve for x:
7(x - 2) = 11(x + 4)
7x - 14 = 11x + 44
-4x = 58
x = -58/(-4)
x = 14.5
Since we're dealing with a discrete quantity (the number of Munchkins), we can conclude that the original box contained 14 Munchkins.