Question 1101086
Answer:
<b>
Yellow:  168
Orange: 219
Black:     93
</b>
—
Check:  168 + 219 + 93 = 480
   and:  168+18 = 186
             219-33 = 186
             2(93) = 186


—
The workout starts from  
480 = (Y - 18) + (O + 33) + (1/2)B    (where each letter = FINAL number of beads of that color)
465 = Y + O + B   (*) 
and noting Y=O=B at this point, which gives   Y = O =  B = 186  (**)
—
Now to find the ORIGINAL number of each color bead, (using lower case y,o,b), just reverse the manipulations given in the problem statement:
y = Y-18 = 186-18 = 168
o = O+33 = 186+33 = 219
b = (1/2)B = 186/2 = 93

——
 EDIT:  Dear student, I see why you are wondering how I got to Y=O=B=186.   The equation (* above) 
should have been written:
                    480 = (Y-18) + (O+33) + (1/2)B
                    465 = Y + O + (1/2)B
and the three quantities that are equal are  Y = O = B   so

   465 = Y + Y + (1/2)Y = (5/2)Y  —> Y=186  
 and that means Y = O = B = 186.

Sorry, I had that step proper on paper but typed it wrong.