Of the black and blue pens in the desk, 18 are black. The ratio of black pens to blue pens is 2:3. Remove 3 pens, what is the new ratio of black pens to blue pens?

2:3 = 18:x

so, x=27, the no. of blue pens.

Now, you have to decide the color(s) of the 3 pens removed to figure the new ratio.

To solve this problem, let's calculate the number of blue pens in the initial setup.

Given that the ratio of black pens to blue pens is 2:3, we can set up the following equation:

2x = 18

Where x represents the common ratio factor. By solving this equation, we find:

x = 9

Now, let's calculate the initial number of blue pens:

3x = 3 * 9 = 27

Therefore, in the initial setup, there were 18 black pens and 27 blue pens in the desk.

Next, we remove 3 pens. Let's subtract 3 from both the initial number of black pens and the initial number of blue pens:

New number of black pens = 18 - 3 = 15

New number of blue pens = 27 - 3 = 24

Finally, let's determine the new ratio of black pens to blue pens:

New ratio of black pens to blue pens = 15:24

Simplifying this ratio, we divide both sides by the greatest common divisor, which in this case is 3:

New ratio of black pens to blue pens = 5:8

Therefore, after removing 3 pens, the new ratio of black pens to blue pens is 5:8.

To determine the new ratio of black pens to blue pens after removing 3 pens, we need to first calculate the initial number of blue pens.

Given that the ratio of black pens to blue pens is 2:3, we can set up a proportion to solve for the number of blue pens:

2/3 = 18/x

To solve for x (the initial number of blue pens), we can cross-multiply:

2x = 3 * 18
2x = 54
x = 54/2
x = 27

So, initially, there were 18 black pens and 27 blue pens on the desk.

If we remove 3 pens, we subtract 3 from both the black and blue pen counts. Thus, the new numbers of black and blue pens are 18-3 = 15 and 27-3 = 24, respectively.

Therefore, the new ratio of black pens to blue pens is 15:24, which can be simplified to 5:8 by dividing both numbers by the greatest common divisor, which is 3.

Hence, the new ratio of black pens to blue pens after removing 3 pens is 5:8.