Lets say a group of children are playing two different sports. 1/5 of them play baseball. 2/3 play football. 1/7 of them play both sports. 50 others do not play at all. How many children were there total?
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The fraction of children playing at least one sport is $\frac 15 + \frac 23 - \frac 17 = \frac{76}{105}$ (we need to subtract $\frac 17$ because in the sum you counted twice the children playing both sports).
The fraction corresponding to the $50$ children not playing any sport is $1-\frac{76}{105}=\frac{29}{105}$. Trying to solve $\frac{29}{105}x=50$, where $x$ is the total number of children, yields to a non-integer solution, pointing to a mistake in the text.
SoniaP
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You are absolutely right. I didn't finish the calculation, thus I didn't realise that the solution is not integer. Seems pointing towards a mistake in the question... – SoniaP Jun 01 '20 at 21:15
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where did you get the 29/105? You're right that this is probably a mistake, but your answer is still useful. – BobaJFET Jun 01 '20 at 22:20
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@StrugglingStudent117 In the answer you can find $1-\frac{76}{105}$. – SoniaP Jun 01 '20 at 22:39