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?
2026-03-28 00:25:45.1774657545
Difficult problem finding a total given only percentages.
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1
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.