There are caps in a box. 1/6 of them are red, 1/3 are blue, and 3/7 of the remainder are green. If there are 27 green caps, how many caps are there altogether?

Question

This is a word problem with fractions turning into whole numbers.

Answer 1

Yes, there are 126 caps.

Begin by drawing a circle, and dividing it into thirds. One third is blue and one sixth (half of a third) is red.  The total of these two areas is a half of the circle. 

 

If 3/7 of the remaining caps (27 caps) are green, then you need to find out what 1/7 is. That would be 9.  

So 7/7 of that segment would be 63 caps in total. Therefore, half of the circle has 63 caps, and the other half of the circle has 63 more. Total = 126 caps. 

 

If you draw the circle diagram at the beginning, you'll be able to understand it using the visual. 

Answer 2

1-(7/42+14/42)=remainder=(1/2)

3/14 are green

 

So if there are 27 green caps, then 1/14 of total caps would be 9 caps (i.e. 1/3 of 3/14)

 

Now we multiply 1/14 by 14 to get 14/14, so we multiply 9*14 = 126 total caps.

 

There are 126 caps.