SOLUTION: 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

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.
RELATED QUESTIONS
There is a specific number of pens available for three students. The first student takes... (answered by ramkikk66)
your are purchasing pens and pencils to be sold at the school store. You need a total of... (answered by macston)
A school bought red & blue pens in separate boxes.all boxes of red pens held the same... (answered by Theo)
Bob has a box in front of him. There are 6 red pens, 4 blue pens, and 2 green pens (answered by ewatrrr)
there is a box of pens and pencils 64 percent are pens. what is the ratio of pens to... (answered by ikleyn)
A college bookstore ordered six boxes of red pens. The store sold 39 red pens last eek... (answered by stanbon,lynnlo)
There are 10 blue pens, 15 red pens and 3 green pens. .write the ratio of blue pens to... (answered by macston)
it costs $120 to manufacture 50 pens in one day and $320 to produce 150 pens in one day.... (answered by Boreal)
There are 12 pens in a pack. 7 of the pens are blue and 5 of the pens are red. Three pens (answered by stanbon)