There are only blue pens, green pens and red pens in a box. The ratio of the number of blue pens to the number of green pens is 2/5 The ratio of the number of green pens to the number of red pens is 4/1 There are less than 100 pens in the box. What is the greatest possible number of red pens in the box?

To solve this problem, we need to understand the ratios given and how they relate to the total number of pens in the box.

1. The ratio of blue pens to green pens is 2:5. This means for every 2 blue pens, there are 5 green pens.

2. The ratio of green pens to red pens is 4:1. This means for every 4 green pens, there is 1 red pen.

To find the greatest possible number of red pens, we need to find a common multiple of the green pens in both ratios. The least common multiple of 5 and 4 is 20.

So, let's assume there are 20 green pens.

According to the first ratio, there would be (20/5)*2 = 8 blue pens.

According to the second ratio, there would be (20/4)*1 = 5 red pens.

Adding these up, we get a total of 8 blue + 20 green + 5 red = 33 pens.

However, the problem states there are less than 100 pens in the box.

To maximize the number of red pens, we can multiply the number of each type of pen by the same factor.

The largest factor we can multiply by while keeping the total number of pens under 100 is 3.

So, we have 83 = 24 blue pens, 203 = 60 green pens, and 5*3 = 15 red pens.

Therefore, the greatest possible number of red pens in the box is 15.