Shifting of xyz
Algebra
Level
pending
If xyz is a 3 digit number and XYZ - ZYX = ZXY Find the number xyz.
The answer is 954.
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1 solution
From the equation xyz-zyx=zxy, we got 100 x+10 y+z-100 z-10 y-x = 100 z+10 x+y.
When we solve the equation you got
89*x = y + 199z
1 <= x <= 9 and 0 <= y,z <= 9
Now we are trying values for x (from 1 to 9) so that 89*x/199 has remainder less or equal to 9.
y is eqaul to remainder of 89 x/199 (if the remainder is less or equal to 9) and z is quotient of 89 x/199, but rounded.