Question 1121545: The total number of pens in boxes X Y Z is 300.Y has 50 percent of the pens in Z. Bob takes out one third of the pens in X trebles the number of pens in Y and puts 40 more pens in Z. Now each box has the same number of pens. Find the total number of pens now.
thanks
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x+y+z=300
y=(1/2)z
(2/3)x=3y=(z+40)
(2/3)x=(3/2)z=z+40
can solve for z
(1/2)z=40
z=80 pens
y=40 pens
(2/3)x=120 pens, x=180 pens (180, 40, 80)
Now they each have 120 pens, and the total is 360 pens. (120, 120, 120)
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Box Y has half as many as box Z, so...
let n = number in box Y
then 2n = number in box Z
Since the total number in the three boxes is 300...
then 300-3n = number in box X
Now Bob takes 1/3 of the pens out of box X; the number now in box X is
(300-3n)-(1/3)(300-3n) = 200-2n
He also triples the number in box Y; the number now in box Y is 3n.
We know that X and Y now have the same number, so
200-2n = 3n
200 = 5n
n = 40
The number now in boxes X and Y is 3n = 200-2n = 120.
Then, since we know all three boxes now have the same number, the total now is 360.
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