2 3 of the pens in a box are blue 1 3 of the remainder are black and the rest are red if there are 34 red pens in the box how many pens are there in the box altogether?

Answer 1

Let's say there are x pens in the box.
There are 2/3 * x = (2/3)x blue pens in the box.
The remainder, which is x - (2/3)x = (1/3)x pens, is not blue.
There are 1/3 * (1/3)x = (1/9)x black pens in the box.
The total number of red, black, and blue pens in the box is (1/9)x + (1/3)x + (2/3)x = 34 pens.
Combining like terms, we get (1/9 + 1/3 + 2/3)x = 34 pens.
Simplifying the left side of the equation gives (4/9 + 2/3)x = 34 pens.
Combining like terms again, we get (10/9)x = 34 pens.
Dividing both sides by (10/9), we get x = (34 * 9)/10 = 306/10 = <<34=34>>34 pens. Answer: \boxed{34}.