Final answer:
To find the number of pupils in the class, we can first determine the number of remaining pupils. We set up an equation using the given information and solve for 'x', but the resulting solution is not valid. There is likely a mistake in the problem statement.
Step-by-step explanation:
To find the number of pupils in the class, we can first determine the number of remaining pupils. Since there are 12 pupils in the computer class, the remaining pupils would be the total number of pupils minus 12. Let's represent the total number of pupils in the class as 'x'.
So, x - 12 is the number of remaining pupils. Since 3/4 of the remaining pupils are in the science club, we can multiply x - 12 by 3/4 to find the number of pupils in the science club: (3/4)(x - 12).
Now, we know that 1/5 of the pupils are neither in the computer nor science club. We can subtract this number from the total number of pupils to find the number of pupils in either the computer or science club: x - (1/5)x.
Finally, we can set up an equation using the information above and solve for 'x':
x - 12 + (3/4)(x - 12) = x - (1/5)x
Simplifying the equation:
5x - 60 + 15x - 180 = 5x - (x/5)
Combining like terms:
20x - 240 = 25x - x/5
Multiplying through by 5 to eliminate the fraction:
100x - 1200 = 125x - x
Combining like terms:
100x - 1200 = 124x
Subtracting 124x from both sides:
-24x - 1200 = 0
Adding 1200 to both sides:
-24x = 1200
Dividing both sides by -24:
x = -50
Since the number of pupils cannot be negative, this solution does not make sense in the context of the problem. Therefore, we need to reject this solution. There is no valid solution to the problem. It is likely that there is a mistake in the problem statement.