+80 In a class, 1/4 of the pupils and an additional 3 pupils like dancing. 1/3 of the remaining class less 3 pupils like swimming. The remaining 21 pupils in the class like jogging. How many pupils are there in the class?
+191 First, I not entirely sure what this phrase means. "1/3 of the remaining class less 3 pupils like swimming." the less 3 pupils is very confusing, so I will assume it's a typing mistake or something and understand it as 3 pupils less than 1/3 of the remaining class.
Now, let's start from there.
I'm going to set all the pupils in the class(which is also what the question is asking for!) as our variable.
1/4x +3 like dance
1/3 of (x-1/4x-3) -3 which goes to 1/4x-4 like swimming
and the rest, which is x - (1/4x +3) - (1/4x - 4) = 1/2x+1 accounts for 21 pupils and they like jogging.
this leaves us with 1/2x = 20 and x = 40, thus there are 40 pupils in this class.
+36916 x = total pupils
1/4x +3 + 1/3(x - 1/4 x -3) -3 + 21 = x
1/4x + 1/3x - 1/12x + 3-1-3+21 = x
1/2 x +20 = x
1/2x = 20
x = 40
