There are some caps in a box. 1/6 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 all together?

3/7 (x - x/6 - x/3) = 27

x = 126

To find the total number of caps, we need to calculate the sum of all the different colors of caps.

Let's start by finding the number of green caps. We know that 3/7 of the remaining caps after red and blue are green. So, we can set up the equation:

(3/7) * Remaining_caps = 27

To isolate "Remaining_caps," we need to multiply both sides of the equation by 7/3:

Remaining_caps = (27 * 7/3) = 63

Now we know that the remaining caps (after red and blue) are 63.

Next, we need to find the total number of caps, including red and blue. We already know that 1/6 of the caps are red and 1/3 are blue.

Let's calculate the number of red caps:

Red_caps = (1/6) * Total_caps

And the number of blue caps:

Blue_caps = (1/3) * Total_caps

To find the Total_caps, we sum up the number of red, blue, and remaining caps:

Total_caps = Red_caps + Blue_caps + Remaining_caps

Substituting the equations:

Total_caps = (1/6) * Total_caps + (1/3) * Total_caps + 63

To solve this equation, we can multiply both sides by 6 to eliminate the fractions:

6 * Total_caps = Total_caps + 2 * Total_caps + 378

Simplifying the equation:

6 * Total_caps = 3 * Total_caps + 378

Subtracting 3 * Total_caps from both sides:

3 * Total_caps = 378

Dividing both sides by 3:

Total_caps = 378 / 3

Total_caps = 126

Therefore, there are a total of 126 caps in the box.