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# FRACTIONS

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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?

Aug 1, 2021

#1
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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.

Aug 1, 2021
#2
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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

Aug 1, 2021