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

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 are musicians but not singers. if there are 150 singers altogether and 40 men are both musicians and singers.

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

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

Pop(400) { ((270(Men) { ((130(Muscian) { ((40(Singer))),((90(Not))) :})),((140(Not) { ((10(Singer))),((130(Not))) :})) :})),((130(Wom.) { ((70(Muscian) { ((40(Singer))),((30(Not))) :})),((60(Not) { ((60(Singer))),((0(Not))) :})) :})) :} Answer:30 women are muscians but not singers. [Abdulhalim Ghadady]

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

Commented by Saham last updated on 02/Mar/17

wow, i really appreciate. God bless you sir.

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

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