if the ratio between the number of red pens is more than the number of blue pens is 2:5 and the number of blue pens is more than the number of red pens by 6 pens then the sum of all pens is ............

Let's solve this step by step:

1. Let's denote the number of red pens as R and the number of blue pens as B.

2. According to the problem, the ratio of red pens to blue pens is 2:5. This can be written as R/B = 2/5.

3. The problem also states that the number of blue pens is more than the number of red pens by 6. This can be written as B = R + 6.

4. Now we can substitute B from the second equation into the first equation: R/(R + 6) = 2/5.

5. If we cross-multiply, we get 5R = 2(R + 6).

6. Simplifying this equation gives 5R = 2R + 12.

7. Subtracting 2R from both sides gives 3R = 12.

8. Dividing both sides by 3 gives R = 4. So, there are 4 red pens.

9. Substituting R = 4 into the equation B = R + 6 gives B = 4 + 6 = 10. So, there are 10 blue pens.

10. The sum of all pens is R + B = 4 + 10 = 14.

So, the total number of pens is 14.

Let's solve this step by step:

1. Let's denote the number of red pens as R and the number of blue pens as B.

2. According to the problem, the ratio of red pens to blue pens is 2:5. This can be written as R/B = 2/5.

3. The problem also states that the number of blue pens is more than the number of red pens by 6. This can be written as B = R + 6.

4. Now we can substitute B from the second equation into the first equation. This gives us R/(R + 6) = 2/5.

5. To solve for R, we can cross multiply to get 5R = 2(R + 6).

6. Simplifying this gives 5R = 2R + 12.

7. Subtracting 2R from both sides gives 3R = 12.

8. Dividing both sides by 3 gives R = 4.

9. Substituting R = 4 into the equation B = R + 6 gives B = 4 + 6 = 10.

10. Therefore, the total number of pens is R + B = 4 + 10 = 14.