Question
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?
Answers
GPT 3.5
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}.
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}.