In a box of coloured pencils 1/6 are blue, 5/12 are green, 1/3 are red and the remainder of 108 are yellow. How many pencil are in the box?

1/6 = 2/12

5/12 = 5/12
1/3 = 4/12

2/12 + 5/12 + 4/12 = 11/12
so
1/12 = yellow

X pencils in the box.

x/6 + 5x/12 + x/3 + 108 = X.
2x/12 + 5x/12 + 4x/12 + 108 = X,
11x/12 + 108 = X,
X = 1296.

To find the total number of pencils in the box, we need to add up the fractions and the remainder:

1/6 (blue) + 5/12 (green) + 1/3 (red) + remainder = 108

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12:

2/12 + 5/12 + 4/12 + remainder = 108

Now we can add the fractions together:

11/12 + remainder = 108

To solve for the remainder, we need to subtract 11/12 from both sides of the equation:

remainder = 108 - 11/12

To subtract 11/12 from 108, we need to convert 108 into a fraction with a denominator of 12:

remainder = (108 * 12) / 12 - 11/12

remainder = 1296/12 - 11/12

remainder = 1285/12

Now, let's find the value of the remainder:

remainder = 1285/12 = 107 remainder 1

So, the remainder is 1.

Finally, we can find the total number of pencils by adding the remainder to the sum of the fractions:

108 + 1 = 109

Therefore, there are 109 pencils in the box.

To find the total number of pencils in the box, we need to add up the fractions representing the different colors of pencils and find their common denominator.

Let's calculate the number of blue pencils:
1/6 of the pencils are blue. To find the number of blue pencils, we need to multiply 1/6 by the total number of pencils. So, the number of blue pencils is (1/6) * x, where x represents the total number of pencils.

Next, let's calculate the number of green pencils:
5/12 of the pencils are green. Similarly, we multiply 5/12 by the total number of pencils to find the number of green pencils. Therefore, the number of green pencils is (5/12) * x.

Now, let's calculate the number of red pencils:
1/3 of the pencils are red. By multiplying 1/3 by the total number of pencils, we can find the number of red pencils. Hence, the number of red pencils is (1/3) * x.

Finally, we know that the remainder of 108 pencils is yellow. Since we have already accounted for the blue, green, and red pencils, the number of yellow pencils is the remaining number after subtracting the blue, green, and red pencils from the total. Therefore, the number of yellow pencils is x - (blue pencils + green pencils + red pencils).

To find the total number of pencils, we need to sum up the quantities of all the different colored pencils:
Total number of pencils = number of blue pencils + number of green pencils + number of red pencils + number of yellow pencils

Substituting the values we have calculated, we get the equation:
x = (1/6) * x + (5/12) * x + (1/3) * x + (x - [(1/6) * x + (5/12) * x + (1/3) * x])

Now, we can solve this equation to find the value of x, which represents the total number of pencils in the box.