A bottle of ink was 2/3 full.When 7 pens were filled with ink from the bottle and 2 pens full of ink was poured into it, it was 1/4 full.How many pens can be filled with the full bottle of ink?

If the bottle holds b and a pen holds p, then we are told

2b/3 - 7p + 2p = x/4
5b/12 = 5p
b = 12p

To solve this problem, we need to determine how much ink is poured into the bottle each time a pen is filled and how much ink is in the full bottle.

Let's assume that each pen can hold an equal amount of ink.

1. We're given that when the bottle is 2/3 full, it corresponds to some number of pens being filled.
2. Next, we're told that when 7 pens are filled with ink from the bottle, and then 2 pens full of ink are poured back into it, the bottle becomes 1/4 full.

Let's represent the full bottle as "x" pens.

1. 2/3 of the bottle corresponds to 2/3 * x pens.
2. When 7 pens are filled, it leaves 2/3 * x - 7 pens of ink in the bottle.
3. Next, 2 pens full of ink are poured back into the bottle, which increases the ink level.
So, the equation becomes (2/3 * x - 7) + 2 pens = 1/4 * x pens.

Now, we can solve the equation:

(2/3 * x - 7) + 2 = 1/4 * x

To simplify the equation, we can multiply everything by 12 to get rid of the denominators:

12 * (2/3 * x - 7) + 12 * 2 = 12 * (1/4 * x)
8x - 84 + 24 = 3x
8x + 24 = 3x + 84
5x = 60
x = 12

Therefore, the full bottle of ink can fill 12 pens.

Let's break down the problem step-by-step:

Step 1: Initial ink level
Given that the bottle of ink was initially 2/3 full.

Step 2: Ink taken out and added
When 7 pens were filled with ink from the bottle, the ink level would decrease. Additionally, 2 pens full of ink were poured back into the bottle, which would increase the ink level.

Step 3: Final ink level
The final ink level is mentioned as 1/4 full.

Now, let's calculate the ink level at each step:

Step 1:
Initial ink level = 2/3

Step 2:
Ink taken out = 7 pens
Ink added back = 2 pens
Net change in ink level = -7 + 2 = -5 pens

Step 3:
Final ink level = 1/4

To find the number of pens that can be filled with a full bottle of ink, we need to calculate the net change in ink level per pen.

Net change in ink level per pen = (Initial ink level - Final ink level) / (Number of pens)

Substituting the values:

(-5 pens) / (Number of pens) = (2/3 - 1/4)

To solve for the number of pens, we can cross multiply:

(-5) * (4) = (2/3 - 1/4) * (Number of pens)

-20 = (8/12 - 3/12) * (Number of pens)

-20 = (5/12) * (Number of pens)

To isolate the Number of pens, we divide both sides by (5/12):

Number of pens = -20 / (5/12)

Number of pens = -20 * (12/5)

Number of pens = -48

However, it doesn't make sense to have a negative number of pens. Therefore, it seems like there is an error in the information or the calculations. Please double-check the problem and attempt the calculations again.