Question

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?

Answer 1

15 red pens

Explanation:

We can multiply the first ratio by 4 to give 20 as the number representing green pens:

blue : green = 8 : 20

We can multiply the second ratio by 5 to give 20 as the number representing green pens:

green : red = 20 : 5

Then the combined ratios are ...

blue : green : red = 8 : 20 : 5 . . . . . . . . . total of 33 "ratio units"

If each "ratio unit" represents 3 pens, then there would be a total of 99 pens in the box. That would mean there are at most 5×3 = 15 red pens.