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.

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!

To find out how many caps there are in total, we'll break down the information step by step:

1. Start with the given information: We know that 1/6 of the caps are red, 1/3 are blue, and 3/7 of the remaining (non-red and non-blue) caps are green.

2. Let's calculate the number of green caps first: Given that there are 27 green caps and that 3/7 of the remaining caps are green, we can determine the total number of remaining caps.

To do this, we'll set up an equation:
(3/7) * x = 27, where x represents the total number of remaining caps.

Solving for x, we multiply both sides of the equation by 7/3:
x = 27 * (7/3)
x = 63

Therefore, the total number of remaining caps is 63.

3. Now, let's find the number of red and blue caps: We are given that 1/6 of the caps are red and 1/3 are blue.

For red caps, we'll calculate (1/6) * 63:
(1/6) * 63 = 10.5

However, we can't have a fraction of a cap, so we need to round this number. Since it is closer to 11, we'll consider it as 11 red caps.

Similarly, for blue caps: (1/3) * 63 = 21 caps.

4. Finally, let's find the total number of caps: We have the number of red caps, blue caps, and the remaining caps (green caps). To obtain the total, we add these numbers together:
Total = Number of red caps + Number of blue caps + Number of green caps

Total = 11 + 21 + 27 = 59

Therefore, there are a total of 59 caps in the box.