Each of , and is an integer. If , , and , what is the value of ?
CEMC Gauss (Grade 8), 2019
Pick one
Solution
The first scale shows that 
has the same mass as 
.
The second scale shows that 
has the same mass as 
.
Therefore, the sum of the masses of 
and 
is equal to the sum of the masses of 
and 
.
That is, the equal-arm scale shown below is balanced.
The left and right sides of this scale each contain a 
, and the scale remains balanced if one 
is removed from each side of the scale (since they are equal in mass).
That is, the equal-arm scale shown below is balanced.
Therefore of the answers given, 
has the same mass as 
.
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