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Balancing Act
 
Q Scales #1 and #2 are in perfect balance. How many Xs must you put on the right side of Scale #3 to make it balance?

Scale #1
Left side: XXYZ Right side: XXXXY
Scale #2
Left side: YYYY Right side: XXZZ
Scale #3
Left side: YYZ Right side: ?


 
A 5 Xs. If you know algebra, you can figure this out by setting up an equation, expressing Y and Z in terms of X's. But you don't need to use algebra if your thinking goes like this:
  1. From Scale #1, you can figure out that Z=2X, because the Z on the left side has been replaced by 2 Xs on the right side.
  2. Next, say that X=2 and Z=4. That would put a 12 on the right side of Scale #2, which means that Y must equal 3 to make the left side of Scale #2 the same as the right side (4×3=12).
  3. Now you know that the left side of Scale #3=10 (3+3+4=10). Since X=2, the right side of Scale #3 must have 5 Xs in order to equal 10 (5×2=10).
By the way, it doesn't matter which numbers you use. Just so you make sure that Z=2X, you'll always come out with 5 Xs on the right side of Scale #3. Go ahead-try it with X=4 and Z=8, and you'll see.

Source: Barnes and Noble,Mensa Mind Games for Kids, p.18