Question Number 104972 by 1549442205PVT last updated on 25/Jul/20
$$ \\ $$$$\mathrm{In}\:\mathrm{the}\:\mathrm{a}\:\:\mathrm{sport}\:\mathrm{camp},\:\mathrm{65\%}\:\mathrm{children}\:\mathrm{know} \\ $$$$\mathrm{playing}\:\mathrm{the}\:\mathrm{football},\mathrm{70\%}−\mathrm{in}\:\mathrm{voleyball},\mathrm{75\%}−\mathrm{in} \\ $$$$\mathrm{basketball}.\mathrm{What}\:\mathrm{is}\:\mathrm{least}\:\mathrm{number}\:\mathrm{of}\:\mathrm{children}\:\mathrm{who} \\ $$$$\mathrm{know}\:\mathrm{playing}\:\mathrm{all}\:\mathrm{above}\:\mathrm{three}\:\mathrm{sport}\:\mathrm{games}? \\ $$$$\left(\mathrm{Answer}\:\mathrm{10\%}\right) \\ $$
Answered by mr W last updated on 25/Jul/20
$${simple}\:{way}\:{without}\:{using}\:{set}\:{theory}: \\ $$$$ \\ $$$${N}_{{F}} ={children}\:{playing}\:{football}\:{only} \\ $$$${N}_{{F},{V}} ={children}\:{playing}\:{both}\:{football}\:{and}\:{volleyball} \\ $$$${N}_{{F},{V},{B}} ={children}\:{playing}\:{all}\:{three}\:{sports} \\ $$$${N}_{{F}} +{N}_{{F},{V}} +{N}_{{F},{B}} +{N}_{{F},{V},{B}} =\mathrm{65}\:\:\:...\left({i}\right) \\ $$$${N}_{{V}} +{N}_{{F},{V}} +{N}_{{V},{B}} +{N}_{{F},{V},{B}} =\mathrm{70}\:\:\:...\left({ii}\right) \\ $$$${N}_{{B}} +{N}_{{F},{B}} +{N}_{{V},{B}} +{N}_{{F},{V},{B}} =\mathrm{75}\:\:\:...\left({iii}\right) \\ $$$${i}+{ii}+{iii}: \\ $$$${N}_{{F},{V},{B}} +\mathrm{2}\left({N}_{{F}} +{N}_{{V}} +{N}_{{B}} +{N}_{{F},{V}} +{N}_{{F},{B}} +{N}_{{V},{B}} +{N}_{{F},{V},{B}} \right)−\left({N}_{{F}} +{N}_{{V}} +{N}_{{B}} \right)=\mathrm{210} \\ $$$${N}_{{F},{V},{B}} +\mathrm{2}×\mathrm{100}−\left({N}_{{F}} +{N}_{{V}} +{N}_{{B}} \right)=\mathrm{210} \\ $$$${N}_{{F},{V},{B}} =\mathrm{10}+\left({N}_{{F}} +{N}_{{V}} +{N}_{{B}} \right) \\ $$$${N}_{{F},{V},{B}} \geqslant\mathrm{10} \\ $$$${i}.{e}.\:{at}\:{least}\:\mathrm{10\%}\:{children}\:{know} \\ $$$${playing}\:{all}\:{three}\:{sport}\:{games}. \\ $$
Commented by 1549442205PVT last updated on 25/Jul/20
$$\mathrm{Great}!\mathrm{Thank}\:\mathrm{you}\:\mathrm{Sir}! \\ $$
Commented by Rasheed.Sindhi last updated on 25/Jul/20
$$\mathcal{S}{uperb}!\:\mathcal{E}{legant}!\:\mathcal{M}{rW}\:\mathcal{S}{ir}! \\ $$