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Dear Mitch,

Can you put up one of those balance scale problems with some kind of New Years' theme to it?

Thank you,

Michael M.


Dear Michael M.,


Here it is. . .


A series of weighings is shown here.  The items on the scales are party hats, noisemakers, and plastic cakes to decorate a room where a party is going to be held.

The first two scales (scale A and scale B) are balanced and complete.  But the third scale (scale C) is not.

QUESTION:  Based on what you see below, how many of the plastic cakes would you need to place on the right-hand side of scale C in order to form a balance with the 3 hats and the 3 noisemakers on the left-hand side of that scale? 

Good Luck!

Happy Holidays,


New Years Eve Math Challenge