Question

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

Answer 1

reds and blues = 1/6 + 1/3 = 1/2

so (3/7)(1/2) or 3/14 are green

3/14 of something is 27
(3/14)x = 27
3x = 378
x = 126

check:
reds = (1/6)(126) = 21
blues = (1/3)(126) = 42
leaving 126-21-42 or 63
greens = (3/7)(63) = 27 , checks out ok!