Question 1101086: Hi
a box contained 480 beads of 3 colors. When 18 yellow beads were added,33 orange beads were
taken out and the number of black beads doubled, there were then an equal number of beads of
Each color.
how many beads of each colour were there at first.
Thanks
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Answer:
Yellow: 168
Orange: 219
Black: 93
—
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.
|
|
|
