In-a-cultural-gathering-of-400-people-there-are-270-men-and-200-musicians-Of-the-latter-80-are-singers-60-of-the-women-are-not-musicians-and-220-of-the-men-are-not-singers-How-many-of-the-women-

Question Number 10872 by Saham last updated on 28/Feb/17

$$\mathrm{In}\:\mathrm{a}\:\mathrm{cultural}\:\mathrm{gathering}\:\mathrm{of}\:\mathrm{400}\:\mathrm{people},\:\mathrm{there}\:\mathrm{are}\:\mathrm{270}\:\mathrm{men}\:\mathrm{and}\:\mathrm{200} \\ $$$$\mathrm{musicians}.\:\mathrm{Of}\:\mathrm{the}\:\mathrm{latter},\:\mathrm{80}\:\mathrm{are}\:\mathrm{singers}.\:\mathrm{60}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are}\:\mathrm{not}\:\:\mathrm{musicians} \\ $$$$\mathrm{and}\:\mathrm{220}\:\mathrm{of}\:\mathrm{the}\:\mathrm{men}\:\mathrm{are}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{women}\:\mathrm{are} \\ $$$$\mathrm{musicians}\:\mathrm{but}\:\mathrm{not}\:\mathrm{singers}.\:\mathrm{if}\:\mathrm{there}\:\mathrm{are}\:\mathrm{150}\:\mathrm{singers}\:\mathrm{altogether}\:\mathrm{and}\: \\ $$$$\mathrm{40}\:\mathrm{men}\:\mathrm{are}\:\mathrm{both}\:\mathrm{musicians}\:\mathrm{and}\:\mathrm{singers}. \\ $$

Answered by Abdulhalim Ghadady last updated on 02/Mar/17

$${Pop}\left(\mathrm{400}\right)\begin{cases}{\mathrm{270}\left({Men}\right)\begin{cases}{\mathrm{130}\left({Muscian}\right)\begin{cases}{\mathrm{40}\left({Singer}\right)}\\{\mathrm{90}\left({Not}\right)}\end{cases}}\\{\mathrm{140}\left({Not}\right)\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\mathrm{10}\left({Singer}\right)}\\{\mathrm{130}\left({Not}\right)}\end{cases}}\end{cases}}\\{\mathrm{130}\left({Wom}.\right)\begin{cases}{\mathrm{70}\left({Muscian}\right)\:\begin{cases}{\mathrm{40}\left({Singer}\right)}\\{\mathrm{30}\left({Not}\right)}\end{cases}}\\{\mathrm{60}\left({Not}\right)\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\mathrm{60}\left({Singer}\right)}\\{\mathrm{0}\left({Not}\right)}\end{cases}}\end{cases}}\end{cases} \\ $$$${Answer}:\mathrm{30}\:{women}\:{are}\:{muscians}\:{but}\:{not}\:{singers}. \\ $$$$\left[\mathscr{A}{bdulhalim}\:\mathscr{G}{hadady}\right] \\ $$$$ \\ $$

Commented by Saham last updated on 02/Mar/17

$$\mathrm{wow},\:\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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