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Word
& Letter Play
Balancing Act
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: ?
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:
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because the Z on the left side has been replaced
by 2 Xs on the right side.
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).
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
